More than half of Wellington City Council's funding for the national museum, Te Papa Tongarewa, is on the line as the council tries to slash its costs for the next 10 years.
The council is proposing to cut its annual grant to Te Papa by $1.25 million to $1 million.
The council has been helping fund Te Papa since 1998.
A Te Papa board member, Evan Williams, says he is disappointed by the proposal.
He says Te Papa is a top-performing investment for the council, returning $41 for every dollar it invests.
"Over 50% of people who visit Wellington go to Te Papa, and interestingly it's the second most frequent activity that visitors to Wellington engage in, after walking the streets of Wellington."
Mr Williams says Te Papa costs $54 million a year to run - $23.5 million of which comes from central government.
The council's spending plans for the next 10 years go to the public for consultation on 16 April.