He says Vermont currently has one of the higher minimum wages in the country at $8.73 an hour, but he says it's not high enough.
He says for people earning the current minimum wage "it's very, very tough to do anything but live in poverty."
Some Vermont lawmakers want to see the wage go to $15 an hour.
Shumlin would not say how much the wage should go up and says it's a discussion that his administration will have with the Legislature.
President Barack Obama said in his State of the Union address Tuesday that he will sign an executive order setting the minimum wage for workers covered by new federal contracts at $10.10 an hour.