Born in Melbourne and taught to sew by his seamstress grandmother, Grant launched his first ready-to-wear line in 1982 and won the Cointreau Young Designer award in 1988. After a detour into sculpture, he relocated to Paris in 1990, opening a boutique on the Rue des Rosiers in 1996 — where his breakthrough came when Naomi Campbell modelled at the shop.
He designed the uniforms for Qantas in 2013. The National Gallery of Victoria has exhibited his work twice, in 2004 and again in a 2025 retrospective after Grant donated more than 200 designs to the gallery.