The museum in Llandudno has been given an extra £35,000 to fund its expansion.
Yesterday members of Conwy's cabinet voted in favour of granting the extra money.
It is hoped that the expanded museum can prove to be a tourism asset and provide a place for people to go during wet weather.
In July 2018, the project was awarded £862,200 by the Heritage Lottery Fund, and the museum has continued its own fundraising efforts to finish the expansion.
But, since costs were obtained last year to give a total project cost of £1.5m, the price tag has gone up to £1.8m, with a gap of £35,000 needed from the council's project match funding provision .
The museum expansion plans will include more exhibition space as well as a community facility which will provide a meeting room for local organisations and as an education centre for visiting school groups.
It will also include improved disabled access and a passenger lift.
Cllr Goronwy Edwards, the cabinet member for economic development, said: "The museum is in need of an upgrade and is planning on becoming a key cultural hub.
"The museum has submitted applications to secure funding from many sources and the funding package is complete, all bar the £35,000 which is a great achievement for which they should be congratulated.
"The museum will be a key site for heritage, culture and tourism and will be an asset to Llandudno .
"It's also an important wet weather attraction for the town."
Greg Robbins, the cabinet member for environment and transportation, also supported the granting of the money.
He said: "This project has been a labour of love for the people involved and has taken many years to get to this point.
"I think it would be absolutely unbelievable if this were to fail. It's a tiny amount of money when they have raised so much and worked so hard
"I look forward to seeing it completed, it will be a great asset for not just Llandudno but Conwy overall."
