Frans Kjellman, Swedish botanist, phycologist and explorer, is known for his work dealing with Arctic algae. He earned his PhD at the University of Uppsala in 1872 before becoming a teacher at Fjellstedt School in Uppsala. He served here until 1878, as well as assisting in the university botanical garden, and in 1883 was appointed professor extraordinary at Uppsala. Ten years later he was made acting professor of botany and in 1899 was appointed to the Borgströmian Professorship of Botany and Practical Economy.

Kjellman undertook several expeditions to the Arctic, travelling to Spitsbergen in 1872-1873, Novaya Zemla and Siberia in 1875 and Finnmark (Norway) in 1876. He travelled with Adolf Erik Nordenskiöld in 1878 on the first ship to complete a crossing of the Northeast Passage (the Vega expedition) and made significant collections of plants (especially marine algae) from the Arctic region. Based on these he authored The Algae of the Arctic Sea: A survey of the species, together with an exposition of the general characters and the development of the flora (1883). He married Hildur Trotzig in 1884, with whom he had a son.

Sources:
O. Franzén, 1975, "Kjellman, Frans Reinhold", Svenskt biografiskt lexicon, 21: 220-222
B.D. Jackson, 1908, Proceedings of the Linnean Society of London, 120: 50-53.