The referendum is part of a pre-election promise by the National Party.
MMP has been the subject of some debate, particularly after Prime Minister John Key said that last year's issues with the Act Party - which is in coalition with the National Party - might turn more people off MMP.
In the current poll, nearly 51 per cent of respondents said they wanted to keep MMP, while 40 per cent wanted a different system. Ten per cent either did not know or refused to answer.
The mood for change was slightly higher among male voters (42 per cent) than female voters (37 per cent).
The details of the referendum and possible review of MMP are set out in the Electoral Referendum Bill, which passed into law just before Christmas.
The bill also put a $300,000 limit on advertising spending, bringing it into line with the proposed third-party advertising limit for general elections. The original bill had no limit.
Aspects of MMP that would be considered in a review include the thresholds for a party to get into Parliament.
The system has been criticised because a vote for a party that falls short of 5 per cent - such as New Zealand First last election - is effectively a wasted vote.
Another criticism has been that a party can bring more MPs into Parliament if a candidate wins an electorate, even if the party falls short of the 5 per cent threshold. Act leader Rodney Hide's hold on Epsom, for example, means the party has five MPs, even though it won fewer party votes than New Zealand First.
A review would also look at the party list, under which a person can be elected to Parliament even if rejected in an electorate, such as Cabinet minister Chris Finlayson or Labour Party frontbenchers Charles Chauvel and Maryan Street.
Excluded from the review would be the Maori seats or the number of MPs.
Five Governments have been elected under MMP since it replaced First Past the Post following a referendum in 1993 that saw 54 per cent support the electoral system.
The Herald-DigiPoll survey had 750 respondents. The margin of error is 3.6 per cent.