The survey, from Republican firm Wenzel Strategies, contradicts a number of previous Democratic polls that showed McConnell to be the nation's least popular senator.
In this new poll, McConnell is seen favorably by 54 percent of respondents, while 44 percent see him unfavorably. And 51 percent believe he's doing an excellent or good job, while 45 percent see him as doing a fair or poor job.
The most recent poll, issued last week by Democratic firm Public Policy Polling, showed him underwater in job approval, with only 44 percent of voters approving of his performance, while 47 percent disapproved.
That poll also showed him tied with potential Senate candidate Alison Lundergan Grimes, Kentucky's secretary of State. But this new poll puts him ahead of her by 7 percentage points, taking 47 percent support to her 40 percent support.
Lundergan Grimes is the Democrats' top recruit in the race, after a number of high-profile Kentucky Democrats turned down a run, but it's unclear whether she'll decide to jump in a race that most agree is likely to be expensive and brutal.
Two other potential contenders also lag McConnell. Heather French Henry, a former Miss America title holder and wife of former Kentucky Lt. Gov. Steve Henry, has expressed interest in the race, and she lags McConnell by 6 percentage points, taking 40 percent support to his 46 percent.
Kentucky environmental lawyer Tom FitzGerald, who is actively exploring a bid, fares the worst against McConnell, with 30 percent support to McConnell's 47 percent. A full 24 percent of voters say they're not sure who they'll vote for in that matchup — likely because 63 percent still have no opinion about FitzGerald.
The new poll also indicates McConnell has a solid base of support going into reelection, as 42 percent of respondents said they'll definitely be voting for McConnell, while only 36 percent said they'll be voting for someone else. Twenty-two percent of respondents said they'd be open to voting for someone other than McConnell.
The Wenzel Strategies survey was conducted among 623 likely voters statewide from June 1-2, and has a margin of error of plus or minus 3.9 percentage points.