Normann is a surname. Notable people with the surname include:
Adelsteen Normann (1848–1918), Norwegian painter
Axel Otto Normann (1884–1962), Norwegian journalist, newspaper editor, theatre critic and theatre director
Emil Normann (1798–1881), Danish painter and naval officer
Jeppe Normann (born 1951), Norwegian fencer
Kristin Normann (born 1954), Norwegian judge and legal scholar
Richard Normann (1943–2003), Swedish management consultant
Runar Normann (born 1978), Norwegian footballer
Sigurd Johan Normann (1879–1939), Norwegian theologian and Lutheran bishop
Wilhelm Normann (1870–1939), German chemist