William Mundy (c. 1529–1591) was a Renaissance English composer of sacred music and father of composer John Mundy.

Mundy was the son of Thomas Mundy, a musician and sexton of the London church St Mary-at-Hill.  William Mundy married Mary Alcock and had two sons, John Mundy, an organist and composer, and Stephen Mundy, a gentleman of the household to James I and Charles I.

In 1543, William Mundy was head chorister of Westminster Abbey, until his voice broke. He was appointed deputy to St Martin, Ludgate in 1547, and from 1548 to 1558 Mundy served as Parish Clerk for the church of St Mary-at-Hill in London (his father Thomas’ employer).  Mundy was appointed Vicar choral to the Chapel Royal in 1559, and appointed a Gentleman of the Chapel in 1564.  He remained in that position for twenty-seven years until his death around early October 1591