Born in Leiden on January 13, 1923, Slijkhuis began his international sports career shortly after World War II, after competing nationally since 1940. In 1946, he won a silver medal in the 5000 m at the European Championships in Oslo.
Two years later, he took part in the Olympics in London, and was a favourite to win a medal. In the 5000 m, he finished third, behind Belgian Gaston Reiff and the legendary Emil Zátopek; nevertheless Slijkhuis was not satisfied. In the 1500 m, his second event, he could have done better, but started his final sprint to the finish line too late to catch the two leading Swedes, who finished narrowly ahead of him. Slijkhuis' achievements were overshadowed by the performances of compatriot Fanny Blankers-Koen, who won four gold medals at the same Olympics.
In 1950, Slijkhuis did win a major title, winning the European title in the 1500 m in Brussels. His second Olympic participation in the 1952 Summer Olympics ended without any successes. Slijkhuis, who won 11 national titles and set 29 Dutch records, ended his career in 1954 due to injuries. He died on June 28, 2003 in Badhoevedorp.