His father was Cornish and his mother was from South Wales. The name "Nepean" is thought to come from the village of Nanpean ("the head of the valley"), in Cornwall.

Nepean married Margaret Skinner, the only daughter of Capt. William Skinner, on 6 June 1782 at the Garrison Church at Greenwich. They had eight children, including Sir Molyneux Hyde Nepean, 2nd Bt., and Maj.-Gen. William Nepean,