Old Museum was originally called the Exhibition Building and Concert Hall. It was built in 1891 for the Queensland National Agricultural and Industrial Association after Brisbane's first exhibition building, which had occupied the land, was destroyed by fire on 13 June 1888. At the time of the fire the building was being used as a skating rink.
The land had been used by the Queensland Acclimatisation Society from 1863-1875.
The new exhibition building was designed by the architect George Henry Male Addison (1857–1922). The style of the building may best be described as progressive eclecticism. It is entered in the Queensland Heritage Register.
The Queensland Government took over control of the building and grounds when the National Association was forced into liquidation by the economic depression in 1897.
In 1899, the Exhibition Hall became home to the Queensland Museum, with the museum remaining in the building until the museum's relocation to the Queensland Cultural Centre in 1986. During the Queensland Museum's 86 years in the building, other parts of the building were used as a Concert Hall and an Art Gallery. Because of the Queensland Museum's long occupancy of the building, the building is now known as the Old Museum.