| Honorific-Prefix: | Sir |
| James Burrow | |
| Order1: | 17th and 19th |
| Office1: | President of the Royal Society |
| Predecessor1: | James Douglas |
| Successor1: | James West |
| Term Start1: | 1768 |
| Term End1: | 1768 |
| Predecessor2: | James West |
| Successor2: | Sir John Pringle |
| Term Start2: | 1772 |
| Term End2: | 1772 |
| Birth Date: | 28 November 1701 |
| Birth Place: | Starborough Castle, Lingfield, Surrey, England, UK |
Sir James Burrow (28 November 1701 – 5 November 1782 at Starborough Castle, Lingfield, Surrey) was an English scholar and legal reporter at Inner Temple, London, and was vice president and twice briefly president of the Royal Society. He was knighted in 1773.
He was elected a Fellow of the Royal Society on 7 April 1737, as "A Gentleman well versed in Natural and Mathematical knowledge". He served as a member of the Royal Society Council from 1752 until 1782, initially as a vice president from 1752, and then as a council member. He twice served briefly as a president of the Royal Society, from October to November 1768 following the death of The Earl of Morton, and July to November 1772, following the death of James West.
As vice president, he was involved in the society's activities in organising the observation of the 1761 Transit of Venus, signing the Articles of Agreement between the Council of the Royal Society and Mr Charles Mason and Mr Jeremiah Dixon for their expedition to Bencoolen in the Island of Sumatra.
As a legal reporter, he wrote and published reports of the decisions of significant cases in the English legal system. At the time, four reporters were formally appointed by the King 'to commit to writing, and truly to deliver, as well the words spoken, as the judgments and reasons thereupon given,' in the courts of Westminster quoted in http://caselaw.lp.findlaw.com/scripts/getcase.pl?navby=CASE&court=US&vol=33&page=591. His work is still cited in law courses.