1903–04 was the 16th season of competitive football for Celtic FC.
They competed in the Scottish First Division[1], in which they placed third.
Celtic won the Scottish Cup with a 3-2 win over Rangers in which Jimmy Quinn scored a hat-trick.
It was Celtic's fourth Scottish Cup victory and, together with their four league titles so far, their 8th major trophy.
Willie Orr, who had been playing for the Glasgow team since 1897, became Celtic's fourth ever captain, as he succeeded Sandy McMahon who had left Celtic the previous season.