However, when it comes to male voters, Romney does much better. Men prefer Romney over Obama by six points, or by 50 to 44 percent, the Post reported.
Virginia is a key battleground state in the coming November election and both Democrats and the GOP are vying for women voters here, and across the nation, to solidify a win.
Obama, especially, needs women "to offset an expected loss to Romney among men," the Post noted.
More from GlobalPost: Obama leads Romney in key swing states: Virginia, Wisconsin, Colorado
As GlobalPost reported, Romney is losing ground not only in Virginia but also in Wisconsin and Colorado, particularly on the economy, according to a Quinnipiac University/CBS News/New York Times poll.
More from GlobalPost: Americans pick Obama over Romney for dinner date, poll says