The museum exists because of a Victorian polymath. Charles Kingsley, the author of The Water-Babies and the historical novel Hereward the Wake, was serving as a canon of Chester Cathedral in 1871 when he helped found the Chester Society for Natural Science, Literature and Art. Kingsley's interests ran from marine biology to social reform to muscular Christianity, and the society he assembled was a similarly broad church. In 1873 it joined forces with the Chester Archaeological Society and the local Schools of Science and Art to raise money for a permanent museum. The architect Thomas Lockwood took the commission. The foundation stone was laid by the Duke of Westminster on 3 February 1885, and the Duke returned to open the building on 9 August 1886.

The museum's name comes from the Grosvenor family, whose heads bear the title Duke of Westminster and who have been the largest landowners in Cheshire for centuries. The 1st Duke's involvement was practical as well as ceremonial; the Grosvenors funded the founding works and lent their name and political weight. The full title of the institution, rarely used in conversation, is The Grosvenor Museum of Natural History and Archaeology, with Schools of Science and Art, for Chester, Cheshire and North Wales. The remit was deliberately regional. North Wales does not have a comparable museum to this day, and Chester acts as cultural capital for a swathe of borderland on both sides of the Dee.

The first curator was Robert Newstead, an entomologist of formidable reputation. He held the post from 1886 to 1913 and then, after a break, returned to serve again from 1922 to 1947. Newstead became Professor Emeritus of Entomology at Liverpool University and a freeman of Chester, and his work shaped the collections in ways still visible today. The City of Chester took over the museum's administration in 1915 and assumed full control of the collections in 1938. The building gained a major extension in 1894 and then sat largely unchanged until a new art gallery was added in 1989. A major reconstruction in 1990 refurbished every public gallery, and the Prince of Wales reopened the museum in 1992. The next year, the Webster Roman Stones Gallery won the North West Museum of the Year award.

Chester was Deva Victrix, the headquarters of the Roman Twentieth Legion, and for two centuries it was one of the most important garrison towns north of the Alps. The Grosvenor Museum holds the finds. The Webster Gallery presents the inscribed stones, the tombstones and altars that the Twentieth's soldiers carved for themselves and their dead. Names recur. Aurelius this, Flavius that, all of them stationed at the western edge of an empire that stretched from Britain to Mesopotamia. The objects are not arranged as trophies. They are arranged as evidence, which is how the Grosvenor has always handled its collections. The 1999 Heritage Lottery Fund award of three hundred thousand pounds went on accessibility improvements and a new shop, not on flash.

Two collections inside the museum are quietly remarkable. The first is twenty-three paintings by Louise Rayner, the Victorian watercolourist who specialised in detailed urban street scenes, particularly of Chester itself. No other public collection holds as many Rayners, and the works form an unmatched visual record of Cheshire in the nineteenth century. The second is six recorders made by Peter Bressan, the French-born woodwind maker who worked in London in the early eighteenth century. Four of those six recorders form the only complete set of Bressan recorders in the country. Recorder makers of his stature are rare in any country, and a complete set is a piece of musical archaeology in itself. The museum sees over one hundred thousand visitors a year, mounts temporary exhibitions, and charges nothing at the door.