At least two men named James Pemberton immigrated to New England in the early 1630's.  They have been confused by some genealogy researchers in the past but their lives have been fairly well documented and luckily they did not live in the same town at the same time. One James lived in Newbury and Boston and the other, our James, lived in Charlestown and Malden.  James of Newbury and Boston was said by Walter Watkins to have come originally from Lawford Essex, and he identified Lancashire as the English home of the Quaker Pembertons who immigrated to Pennsylvania.  The English origins of our James Pemberton are unknown. 
If you do a search of ancestry.com you will find a Dr. William Pemberton and Anne Heaton listed in multiple family trees as the parents of James Pemberton, baptized on 20 March 1607. First of all, there was a James baptized on that date, in London. But his father was identified as John Pemberton.  Not that this really matters because we do not know where James came from. One old genealogy claimed that James was at one time the a Knight and the Mayor of London, this is also incorrect.
It's always fun to be able to trace our ancestors across the pond to their English home, unfortunately this is not the case for James. Maybe someone will trace his roots, but until then, beware of any claims for his ancestry.
coming to america
Well, we don't know from where, but we do know when. James was one of many men who applied for freemanship at the General Court held in Boston on the 19 of October 1630. Although he applied, there is no record of him taking the oath. In fact, there is no record of him at all until three years later, in 1633. It is possible that he returned to England for at time. 
In December of 1633 James was admitted to the town of Charlestown and he was a married man.  His wife Alice was admitted to the church at Charlestown on 31 August 1633, so we know he was back in Massachusetts by then.  Did he return to England to get his wife? What's interesting is that his wife was a church member, but he was not. This meant that he could not take the Freeman's Oath. We do not know anything about Alice, other than her name.
the mystic side
James was given land in Charlestown, but he also received land in the divisions on the Mystic side, which eventually became the town of Malden. In 1640 the 'mystic side' was set apart from Charlestown and became its own town, Malden.
children of james and alice 
Like all reproductive puritans, James and Alice had regularly spaced children, about every two years or so. Unlike most families, they only had four. All four were baptized in Charlestown. Nothing is heard of Alice after the 1642 baptism of John. The only reference to James is his baptism.
1. James, baptized 14 September 1633, no further record, not named in father's will
2. Mary, bp. 3 April 1636, m. abt. 1656 Edmund Barlow
3. Sarah bp. 30 December 1638, m. 30 October 1668, Samuel Gibson
4. John, bp. 24 April 1642, m. by 1668 Deborah Blake
what did he do?
Sometimes the only way to assess what someone was in life is to look at what they left behind in death and this is the for James. The probate and inventory for his estate show a very modest estate valued at only a bit less than eighty five pounds. He owned his house, some land and not a whole lot more.  It does not appear that he had a secondary occupation. Did lack of sons hinder James? Most puritan families were significantly larger than James' and he had only one son alive when he wrote his will. Without the 'free' labor of unmarried sons, James may not have been able to farm as much as his neighbors.
Captain Robert Keayne of Boston and Rumney Marsh Farm, left a bequest of 40 shillings to James Pemberton. Keayne said that James was sometimes his servant but now his partner on his farm. This has led many to believe that this was the James Pemberton of Malden, but it was not. In 1683, James Pemberton, age 51, and his wife Sarah, testified in court that they were tenants on the farm of Robert Keayne. Since our James was long dead in 1683, this cannot be our guy. 
In 1651 an unusual document was generated in Malden in support of their Minister Mr. Matthews. The petition is signed by 31 women, no men, just women. Margaret Pemberton's name appears on that petition. There is no record of the death of Alice, she obviously died sometime after the 1642 birth of her son John and before October of 1651, the date of the petition. Nothing else is known about Margaret Pemberton, only that she survived James. 
James appears in two published court records from Middlesex County. The first was in 1653. He, his wife Margaret and his son in law Edward Barlow were involved in some type of dispute with Richard Dexter, his wife Bridget and their daughter Elizabeth. The issue was to be resolved by a group of local men. 
In 1654 James was a member of jury who performed an inquest into the accidental shooting death of a twelve year old boy. 
James also appeared before the General Court of Massachusetts in a land dispute. He claimed ownership of an Island, known as Pemberton's Island. The Court confirmed that the land was his.
James wrote his will on 23 March 1660. The first bequest he made was to his Edward Barlow, the husband of his daughter Mary. He gave them the upland that they were living on. He also gives them his orchard and fresh meadow, his wife Margaret to get one half of the grass from the meadow while she lived. His daughter Sarah, unmarried at the time was to get ten pounds. His house and the remainder of he estate he split between his son John and his wife, John to have it all on Margaret's death. 
James died about two years later. His estate was in probate on 1 April 1662. Presumably he was buried in Malden. It would seem that James lead a very quiet modest life. He made his mark on his will, so he was not able to write his name. There is no record of him taking the Freeman's Oath or becoming a member of the church. He did not seem to have any civic duties, other than serving on the jury.
 Jeanette T. P. Barnard, "Two James Pembertons," The Essex Genealogist, 19 (February 1999): 206, American Ancestors (http://www.americanancestors.org : accessed 9 November 2015).
 Barnard, "Two James Pembertons."
 Walter K. Watkins, "The Pemberton Family," The New England Historic and Genealogical Register, 46 (1892) :392-396, American Ancestors (http://www.americanancestors.org : accessed 9 November 2015).
 Robert Charles Anderson, The Great Migration Begins: Immigrants to N. E. 1620-1633, Vols. 1-3, (Boston: The New England Historic and Genealogical Society, 1995) p. 1419-1420.
 England, Baptisms, Marriages and Burials 1538-1812, database with images, Ancestry.com (http://www.ancestry.com : accessed 9 November 2015) City of London, St. Augustine Parish, Watling Street, entry for James Pemberton baptism 20 March 1607.
 Anderson, Great Migration Begins, 1420.
 Torrey's New England Marriages to 1700, online database, digital images, American Ancestors (http://www.americanancestors.org : accessed 9 November 2015), entry for James Pemberton and first wife Alice, second wife Margaret.
 J. F. Hunnewell, Records of the First Church of Charlestown, 1632-1789, (Boston: D. Clapp and Sons, 1880), Google Books (http://www.books.google.com : accessed 10 November 2015).
 Anderson, Great Migration Begins, 1420.
 Mellen Chamberlain, Jenny Chamberlain, and William Richard Cutter, A Documentary History of Chelsea: including the Boston Precincts of Winnisimmet, Rumney Marsh and Pullen Point, 1624-1824, Vol 1, (Boston : 1908), 663.
Deloraine Corey, A History of Malden, MA, 1633-1785, (Malden 1899), 134.
 "Middlesex County, Massachusetts Abstract of Court Records, 1643-1674," digital images, American Ancestors (http://www.americanancestors.org : accessed 15 november 2015, 1654 inquest for Caleb Johnson.
 "Middlesex County, Massachusetts Abstract of Court Records, 1643-1674," digital images, American Ancestors (http://www.americanancestors.org : accessed 15 november 2015, 1653 Dispute between James Pemberton and Richard Dexter.