First-past-the-post would win by a nose over MMP if there was a contest between the two systems today.
A Herald-DigiPoll survey asked respondents which of FPP, MMP or "something else" they would choose if there was a referendum today.
First-past-the-post was chosen by 39 per cent - just beating MMP on 35 per cent.
Ten per cent said they would chose something other than FPP or MMP and 16 per cent either refused to say or did not know.
National leader John Key has promised to hold a binding referendum on MMP if he leads the next government, saying voters should get a chance to pass a verdict on the new system now it has been in place for 12 years.
In the poll, National Party supporters were far more likely to want the change back to FPP - 57 per cent chose the old system compared to 22 per cent of Labour supporters.
Unsurprisingly, supporters of NZ First, the Greens and the Maori Party also rejected a change back to FPP. Maori Party voters gave the most ringing endorsement of MMP - 92 per cent chose it, compared to 62 per cent of NZ First and Green Party voters.
The head of Auckland University's political studies department, Raymond Miller, said an approximately even split in support between FPP and MMP was still to be expected.
Conservative and older voters tended to like FPP, whereas younger, more liberal voters had never voted under FPP and backed MMP.
The Herald-DigiPoll survey indicates a major education campaign would be needed to make a third option a viable contender in any future referendum.
Support for an alternative was highest among Green Party supporters - one quarter said they would chose a different system to MMP or FPP, compared with about 10 per cent for National and Labour supporters.
Mr Miller said the result of a referendum could depend on how the public viewed the government in power at the time.
If it was a majority National government and was popular, it could increase support for a system which favoured the two major parties.
If it was unpopular, support for MMP would remain strong.
The poll of 700 was taken between September 15 and 24 and has a margin of error of 3.7 per cent.