He spent his childhood in Sjörup outside Ystad and Gessie south of Malmo and trained under Tage Hansson at Skåne painting school in Malmö from 1940 to 1942 and Fritiof Schüldt at the Royal Academy of Arts in Stockholm from 1943 to 1949. He had his first solo exhibition in Malmö in 1950 and taught painting alongside Staffan Nihlén at the Art School Forum in Malmö between 1964 and 1987. Nordström is known for his anti-war art, especially for the suite In the summer of 1970, a commentary on the Vietnam War and the massacre at My Lai. He was commissioned by the Swedish Parliament to paint a portrait of President Thage G. Peterson. His work is represented at Gothenburg Museum of Art.