Seven out of ten respondents told pollster Sifo they would back moves to change the current legislation.
Christian Democrat voters however deviated from the majority.
"The proposal enjoys overwhelming support but it runs up against equally strong opposition in the Christian Democrats," Sifo's Toivo Sjörén told Svenska Dagbladet.
The results are based on a poll of 1,000 people carried out from January 14th to 17th. Sifo asked: Do you think homosexual couples should be able to legally wed and get married or do you think they should not be able to get married?