2004–05 Albanian Cup (Albanian: Kupa e Shqipërisë) was the fifty-third season of Albania's annual cup competition. It began on 28 August 2004 with the First Preliminary Round and ended on 11 May 2005 with the Final match. The winners of the competition qualified for the 2005-06 first qualifying round of the UEFA Europa League. KF Partizani were the defending champions, having won their fifteenth Albanian Cup last season. The cup was won by KS Teuta.
The rounds were played in a two-legged format similar to those of European competitions. If the aggregated score was tied after both games, the team with the higher number of away goals advanced. If the number of away goals was equal in both games, the match was decided by extra time and a penalty shootout, if necessary.
All fourteen teams of the 2003–04 Superliga and First Division entered in this round, along with Second Round winners. First legs were played on 20 October 2004 and the second legs were played on 27 October 2004.