The Republican-controlled Senate was expected to eliminate the monthly cap in a vote Friday, following the GOP-controlled House in approving the measure, The Washington Post reported.
Republican Gov. Robert F. McDonnell indicated he would sign the bill.
Activists on both sides of the gun-control issue agree that the Virginia state government has grown friendlier toward gun rights since Republicans took control of the statehouse and the governor's mansion.
"It's going pretty well," said Philip Van Cleave, president of the Virginia Citizens Defense League. "It's by no means perfect. There are some good bills that aren't making it, but there are good bills that are. And I think we're seeing much more progress than we've seen the last several years."
Lori Haas, a gun-control activist whose daughter was injured in the 2007 massacre at Virginia Tech in which 33 people, including the gunman, died, told the Post she thought the statehouse was going down the wrong path.
"Obviously, it says something about the Republicans that they pander to special-interest groups instead of law enforcement and the citizens of Virginia," she said.
The cap was enacted in 1993 under Democratic Gov. L. Douglas Wilder to curb the state's role in gun trafficking along the East Coast.
"Now that we have background checks that we didn't have [in 1993], one gun a month has outlived its purpose," said Republican Sen. Charles Carrico, who sponsored the bill.