The poll -- conducted Nov. 15-18 -- found 40 percent of those surveyed said they viewed the retired four-star Army general favorably and 30 percent viewed him unfavorably.
Petraeus resigned Nov. 9 after admitting he had engaged in an extramarital affair.
In five previous surveys from 2007 to 2011 -- mostly when Petraeus was an active duty general directing U.S. military operations in Iraq and Afghanistan -- Gallup found his favorable rating ranged from 47 percent to 61 percent, for an average of 54 percent.
Fifty-one percent of those surveyed last week said they supported Petraeus' decision to resign as director of the CIA. Forty-one percent said they thought he should not have resigned.
Fifty-three percent said they had been following news about the Petraeus scandal very closely (22 percent) or somewhat closely (31 percent.)
Among those who said they had followed the story very closely, 61 percent said he should have resigned and 37 said he should have stayed on the job.
The poll was based on telephone interviews with a random sample of 1,015 adults age 18 and older in all 50 states and the District of Columbia. The margin of error is 4 percentage points.