The project started four weeks behind schedule, but work was nearly back on schedule, Dunedin City Council officials said.
Concrete wall panels made in Ashburton and Timaru for the twin-level building were now being lifted into place by crane, officials said.
Project development manager Bronwyn Simes said she was pleased with construction progress. Lund South was the main contractor, she said.
The site would continue to be busy over the next few weeks, with about 90% of the walls expected to be in place by Christmas.
After the walls and cross beams had been installed, the first-floor concrete slab would be moved into place, with the roof to be added next year.
The new building will provide climate-controlled protection for all the museum's artefacts, and should be completed by August 2009.
Poor storage conditions at the museum have exposed many of Dunedin's heritage treasures to the risk of damage from heat, moisture rust and borer.
The storage building is the first stage of a $35 million museum development project, due for completion in 2012.
