Aldeburgh Museum was established by the Aldeburgh Literary Society in 1912 in a single room behind the Old International Stores in Aldeburgh High Street. It housed a mammoth tusk, stuffed birds and volumes of poetry and other items relating to George Crabbe as well as archaeological material. The collection was greatly enhanced in 1915 with material acquired from the Snape Anglo–Saxon Ship burial.

During the Second World War the collection was boxed up and packed away in the attic of the council offices. Thankfully however in 1955 the council re-established the museum and it moved into a room on the ground floor of the Moot Hall. The Grade 1 listed 16th century timber-framed building, continuously used for local governance since Tudor times, provided an appropriate setting for the museum and formed a prime exhibit itself.

In 1973 a charitable trust, the Aldeburgh Museum Collections Trust, was set up. Since then, through the hard work of the volunteers, it has become an accredited and much-loved local museum.  In 2016 the trust was changed to a Charitable Incorporated Organisation or CIO and is now called the Aldeburgh Museum Charitable Trust.