The bill, which is known as the Civil Marriage Protection Act was passed n a 72-67 vote after a similar billed failed to pass in the chamber last year, according to the New York Times.
The bill will be voted on in the Senate, where similar bills have passed in the past, according the Washington Post.
The bill will likely also be up for referendum in November, where voters will have the last say about the bill before it is scheduled to take effect January 1, 2013, according to the Washington Post.
Many delegats say they have received threats that a yes vote for the same-sex marriage bill would cost them the next election, which is scheduled for 2014, according to the New York Times.
"I've heard all types of threats, that in 214 at the ballot box, there would be revenge, but when that day comes, I know that for the seven openly gay colleagues, if they are able to have the same rights as my wife and I have, then I know that my green vote was the right vote," said Keiffer J. Mitchell Jr., a Democrat from Baltimore, according to the New York Times.