Swanstrom or Swanström is a surname. Notable people with the surname include:
Arthur Swanstrom (1888-1940), American lyricist Dwight A. Swanstrom (1905–1978), American businessman and politician Edward Ernest Swanstrom (1903–1985), American Roman Catholic Titular Bishop of Arba, Auxiliary Bishop of New York J. Edward Swanstrom (1853–1911), American lawyer and politician from New York Jack Swanstrom (born 1961), American educator and film director Karin Swanström (1873–1942), Swedish actress, producer and director