The center of culture and fine arts Hafnarborg was founded in 1983 by Sverrir Magnússon and his wife Ingibjörg Sigurjónsdóttir.

The building was originally designed for chemist Sören Kampmann, who lived and worked in it until 1947. Then Magnússon took possession of the building and created his own museum, which was managed by him for 37 years. On June 1, 1983, the family presented the city with a gift certificate for the building and an extensive collection of art and books. It was stated that the house should be a place of cultural activity and development of the city's life through the placement of an art museum, exhibition halls, and artist's residence, as well as a venue for concerts.

The center for culture and fine arts was officially opened on May 21, 1988. By that time, the building had been redesigned by the architect Ingimar H. Ingimarsson. The official mission of Hafnarborg is the support of cultural activities of city life. The museum houses the Hafnarfjörður art collection and is also responsible for research and exhibitions to ensure that this heritage will continue to be an important part of the history of Icelandic culture and art. Moreover, the museum organizes an international project for artists who want to create their works on the museum's territory.

The Museum hosts a wide variety of exhibitions. There are 10-12 art exhibitions each year. They exhibit works that are significant for the history of Icelandic art: from paintings by its founders to experimental works by contemporary artists. Museum expositions are also studied in detail at lectures and seminars that are regularly held. Hafnarborg strives to have an open dialogue with its visitors, artists, and curators to make exhibitions more dynamic and interesting. It also hosts regular seminars and excursions for children and a lunchtime concert with a focus on classical music once a month.

The museum tries to make a significant contribution to the positive image of the city and the identity of its residents. According to its mission, exhibitions and events should reflect current trends and promote the most significant works. Hafnarborg maintains a dynamic collaboration with artists, museums and other cultural institutions in Iceland and abroad.