The 1903–04 season was the eleventh season in which Dundee competed at a Scottish national level, playing in Division One, where they would finish in 5th place. Dundee would also compete in the Scottish Cup, where they would progress to the quarter-finals and take eventual champions Celtic to two replays before being defeated. This would be the first season where Dundee would wear their now common look of navy shirts, white shorts and navy socks.