Support for the National Party has dropped five points since the last survey in April, according to the latest One News Colmar Brunton Poll.
The poll of 1000 voters was taken in May, following the Budget.
It shows support for the National Party on 49%, Labour on 33%, the Green Party on 7%, the Maori Party on 3.6% and ACT on 1.6%.
Mr Key remains the most preferred prime minister on 46%, 40 points clear of Labour leader Phil Goff, who is on 6%.
The poll also asked people if they thought the economy was going to be in a better or a worse state in the coming year.
Fifty six percent thought it was going to get better, while 26% thought it was going to get worse and 18% thought it would stay about the same.
The poll has a margin of error of plus or minus 3.1%.