Moore had 51 percent support among those polled to Jones' 40 percent. Nine percent were undecided.
The survey polled 3,000 likely voters on Monday and had a margin of error of 2-3 percent.
"I think the challenge for the Jones campaign is bigger than what these numbers show," Jonathan Gray, pollster for Mobile-based Strategy Research, the firm that conducted the poll, told Raycom. "Even if he were able to close the gap, how do you turn out Democrats in a state that hasn't had a viable Democratic Party in almost a dozen years?"
Meanwhile, the poll also found that President Trump had a 55 percent approval rating from those surveyed with 45 percent disapproving. The poll said 93 percent of Moore supporters also backed Trump while just 13 percent of Jones supporters gave a positive approval rating to the president.