1970–71 Albanian Cup (Albanian: Kupa e Shqipërisë) was the nineteenth season of Albania's annual cup competition. It began on August 1970 with the First Round and ended on May 1971 with the Final match. KF Partizani were the defending champions, having won their ninth Albanian Cup last season. The cup was won by Dinamo Tirana. The rounds were played in a one-legged format similar to those of European competitions. If the number of goals was equal, the match was decided by extra time and a penalty shootout, if necessary.