James "Jimmy" B. Niven (born circa 1862) was a Scottish international football player.
Niven was one of two Scottish internationalists from Moffat. The other was James Fraser. While playing for Moffat F.C., Niven was an awarded a full Scotland international cap, for having played in the 8–2 defeat of Ireland on 14 March 1885. The game was played at the second Hampden Park, later known as Cathkin Park, and Alex Higgins of Kilmarnock scored a hat-trick. This was the only full international cap that both players received.