The Museum's first building was constructed in 1915 and opened to the public in 1919 but many Cham sculptures collected in Da Nang, Quang Nam and elsewhere were brought to the site over the preceding twenty years.
The collection was begun by French archaelogists and experts from L’École Francaise d’Extrême Orient (EFEO). Some artefacts were sent to Paris and others to the Ha Noi and Sai Gon (now Ho Chi Minh City) museums, but many typical objects were left in Tourane (now Da Nang).
The establishment of a Cham sculpture museum in Da Nang was first proposed in 1902 by the Department of Archaelogy of EFEO. Henri Parmentier, a prominent archaelogist of the department, made great contributions to the compaign for its construction. The first building was designed by two French architects. M. Deleval and M. Auclair. The Museum has been extended twice, but the character of the original architecture has been well preserved.
The first extension was in the 1930s, with two new galleries providing display space for the objects added in the 1920s and 1930s. Henri Parmentier directed the display based on the areas where the sculptures were found. The 1000 square metre of floor space was arranged into the My Son , Tra Kieu, Dong Duong and Thap Mam galleries and the Quang Tri, Quang Ngai, Binh Dinh, Kon Tum corridors.
In 2002, the Museum was again extended with the two-storey building provide an extra 1000 square metre. The new building provides space for display, storage, a library, restoration workshop and offices for staff.
Before 2007, the Museum was managed by the Museum of Da Nang, and administrative organ in charge of the cities’ museums and heritage. On 02 July 2007, the city authorities affiliated the Da Nang Museum of Cham Sculpture with the Department of Culture, Sport and Tourism.