HMS Kelvin was a K-class destroyer of the Royal Navy laid down by the Fairfield Shipbuilding and Engineering Company, Limited, at Govan in Scotland on 5 October 1937, launched on 19 January 1939 and commissioned on 27 November 1939 with the pennant number F37.

The J, K and N class consisted of 24 destroyers built for the Royal Navy beginning in 1938. They were a return to a smaller vessel, with a heavier torpedo armament, after the Tribal class that emphasised guns over torpedoes. The ships were built in three flotillas or groups, each consisting of eight ships with names beginning with "J", "K" and "N". The flag superior of the pennant numbers changed from "F" to "G" in 1940.