The latest WHAS11/Courier-Journal Bluegrass Poll shows Grimes at 46 percent and McConnell at 42 percent.
McConnell leads his primary challenger, Matt Bevin, by 26 points among registered Republicans.
The poll also shows that President Obama suffers a 60 percent disapproval rating; the same rating McConnell has.
Forty nine percent of voters in the poll said that Obamacare should be repealed, while 44 percent said that the program should be implemented and fixed.
The poll of 1,082 registered voters, of which 404 were registered Republicans, was taken Jan. 30-Feb. 3 and had a 3-percentage-point margin of error.