The League Cup 1980/81 was the 21st edition of the English League Cup , which had existed since 1960 .
The competition started on August 8, 1980 with the first round and ended on April 1, 1981 with the second final at Wembley . The title went to Liverpool FC , who defeated the second division West Ham United in the final after a 1-1 draw in the first game and 2-1 in the replay. Liverpool won the English League Cup for the first time in its second appearance in the final after 1978 . West Ham rose at the end of the season as a second division champion in the First Division .