Daughter of John Cochrane (1687-1720), 4th Earl of Dundonald, and Anne Murray (d. 1710). Married (1729) to Alexander Stewart, 6th Earl of Galloway.
Boswell met Catherine Cochrane, then Lady Galloway, at Galloway House on September 25, 1762, describing her as "a tall stately woman [who] in the last age was reckoned a beauty. [...] She is a High-Church woman in religion, a Jacobite in politics, and has a forbidding stiffness of manners that is very disagreeable. [...] She is very charitable and manages her family with much discretion." On September 26 she gave to Boswell a copy of Essays and Meditations by Dr. James Mackenzie.