The museum opened on 28 October 1978, the 250th anniversary of the birth in the same spot of British naval explorer and circumnavigator Captain James Cook.

Prior to the museum's establishment, there was a granite urn in Stewart Park commemorating the grounds of Marton Hall, Cook's residence.

[3] The museum itself comprises some of the modest Cook-related collections outside of the ownership of the major national and international collections, including household items and a speculative reconstruction of Cook's birthplace cottage that was swept away amid the landscaping process for the Marton Lodge, home to the Rudd family, which stood here until 1793.

There are a series of interactive displays and temporary travelling exhibitions as well as a cafe, gift shop, education suite and resources and archive room.

A second major refurbishment was undertaken in 1998, which included the commission of two modern works of art by Turner Prize nominee Simon Patterson.