The WSB-TV poll found that Mrs. Nunn has 47 percent to 40 percent edge over Mr. Perdue. The libertarian candidate, Amanda Swafford, received 3 percent, and 10 percent of the respondents were undecided.
The winner of the race will replace retiring Sen. Saxby Chambliss.
Mrs. Nunn, the daughter of former Georgia Sen. Sam Nunn, is seen as one of Democrats best bets to flip control of a GOP-held seat. Republicans need to flip six seats to win back the Senate.
The poll, which was released late Friday, showed that Mrs. Nunn has a 52 percent to 34 percent lead among women and a 65 percent edge among black voters.
Mr. Perdue, meanwhile, has a 7 percentage point lead among men and 20-point lead among white voters.