Köster is a German surname. Notable people with the surname include:
Adolf Köster (1883–1930), German politician and diplomat
Bärbel Köster (b. 1957), German athlete
Franz Köster (f. 1940s), German Luftwaffe pilot during World War II
Fritz Köster (1855–1934), German trade unionist
Gaby Köster (born 1961), German actress
Johann Adolf Köster (1550–1630), German pastor and educator
Maartje Köster (born 1975), Dutch cricketer
