Iver Johan Unsgård (26 June 1903 - 30 June 1993) was a Norwegian politician for the Labour Party.
He was elected to the Norwegian Parliament from Sør-Trøndelag in 1958, and was re-elected on two occasions. He had previously been a deputy representative from 1954 to 1957.
Unsgård was born in Tydal and mayor of Tydal municipality during the terms 1945 - 1951, 1951 - 1955 and 1955 - 1958.