It took place between 28 May 1980 and 31 August 1980, with the final played at Laugardalsvöllur in Reykjavik. The cup was important, as winners qualified for the UEFA Cup Winners' Cup (if a club won both the league and the cup, the defeated finalists would take their place in the Cup Winners' Cup).
The 10 clubs from the 1. Deild entered in the last 16, with clubs from lower tiers entering in the three preliminary rounds. Teams played one-legged matches. In case of a draw, the match was replayed at the opposition's ground.
Fram Reykjavik retained their title, winning their fourth Icelandic Cup by beating ÍBV Vestmannaeyjar in the final. The club therefore qualified for Europe.
The 1970 Icelandic Cup was the 11th edition of the National Football Cup.
The 1971 Icelandic Cup was the 12th edition of the National Football Cup. Víkingur Reykjavík were winners.
The 1973 Icelandic Cup was the 14th edition of the National Football Cup.
The 1974 Icelandic Cup was the 15th edition of the National Football Cup.
The 1975 Icelandic Cup was the 16th edition of the National Football Cup.
The 1977 Icelandic Cup was the 18th edition of the National Football Cup.
The 1978 Icelandic Cup was the 19th edition of the National Football Cup.
The 1979 Icelandic Cup was the 20th edition of the National Football Cup.
The 1981 Icelandic Cup was the 22nd edition of the National Football Cup.
The 1982 Icelandic Cup was the 23rd edition of the National Football Cup.
The 1983 Icelandic Cup was the 24th edition of the National Football Cup.
The 1984 Icelandic Cup was the 25th edition of the National Football Cup.
The 1985 Icelandic Cup was the 26th edition of the National Football Cup.
The 1986 Icelandic Cup was the 27th edition of the National Football Cup.
The 1987 Icelandic Cup was the 28th edition of the National Football Cup.
The 1988 Icelandic Cup was the 29th edition of the National Football Cup.
The 1989 Icelandic Cup was the 30th edition of the National Football Cup.
The 1990 Icelandic Cup was the 31st edition of the National Football Cup.
The 1991 Icelandic Cup was the 32nd edition of the National Football Cup.
The 1992 Icelandic Cup was the 33rd edition of the National Football Cup.
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