Gunnar Thoroddsen (pronounced ) (December 29, 1910 – September 25, 1983) was Prime Minister of Iceland from 8 February 1980 to 26 May 1983. Gunnar is the youngest man ever elected to the Althing, Iceland's Parliament. He was 23 years old when he was elected as MP in 1934. He served as an Ambassador of Iceland in Denmark from 1965 to 1969 when he ran for the presidency of Iceland in 1968. He wished to succeed his father in law, Ásgeir Ásgeirsson, who served as president from 1952 to 1968. Gunnar had been mayor of Reykjavík from 1947 to 1959 and minister of finance from 1959 to 1965. He was minister of industry and a social welfare minister in the cabinet of Geir Hallgrímsson August 28, 1974 to June 27, 1978.
Gunnar and Geir were not in agreement and the disagreement led to Gunnar breaking away from the will of the Independence Party with a few members of parliament and forming a cabinet with the Progressive Party and the People's Alliance, that replaced a minority government of Benedikt Sigurðsson Gröndal. By forming his government Gunnar became the oldest Prime Minister in Iceland's history at the age of 69. Gunnar did not run in the 1983 elections for parliament, due to his illness, and ended his involvement in politics when his cabinet was succeeded by Steingrímur Hermannsson's cabinet.
Gunnar Thoroddsen died in September 1983.