He was the son of John Fitzalan, Lord of Arundel, and Isabella, daughter of Roger Mortimer of Wigmore. His father was never formally called Earl of Arundel, but Richard was so addressed due to his possession of Arundel, seat of the old Earls of Arundel.
During the last decade of his life Arundel had commands in a number of English military campaigns, on the Welsh and Scottish marches and in Gascony.
He married Alisona (also known as Alice), daugther of Thomas, marquis of Saluzzo in Italy, and was succeeded by his eldest son Thomas.
{| border="2" align="center"
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|width="30%" align="center"|Preceded by:
John Fitzalan
|width="40%" align="center"|Earl of Arundel
|width="30%" align="center"|Followed by:
Edmund Fitzalan
|}