The Herald-Digi Poll survey found 49 percent would vote to ditch the proportional voting system; 35.8 percent wanted to retain it and 15.2 percent were undecided.
The referendum was a government election pledge.
MMP replaced the first past the post system in 1996 and allowed smaller parties to be represented in Parliament.
Justice Minister Simon Power last month announced a referendum would be held at the next election asking whether voters wish to change the voting system from MMP and what alternative voting system they would prefer, from a list of options.
If the vote was for change a second binding referendum would be held at the same time as the 2014 general election and would run off MMP against the alternative that gained the most votes in the first referendum.
Anti MMP campaigner Peter Shirtcliffe told The New Zealand Herald he wasn't surprised by the strong support for change but said the two stage referendum process was too slow.
"It's an outrage. We should be rearing up on our hind legs about the delay in getting rid of this."
Green co-leader Metiria Turei said some negative responses might reflect concerns with aspects of MMP rather than the whole system.
There was widespread misunderstanding of MMP, she said.
