Castberg is a Norwegian surname. Notable people with the surname include:
Frede Castberg (1893–1977), Norwegian jurist Johan Castberg (1862–1926), Norwegian jurist and politician Johan Christian Castberg (1911–1988), Norwegian illustrator and painter Johan Christian Tandberg Castberg (1827–1899), Norwegian politician Leif Castberg (1876–1950), Norwegian lawyer and politician Oscar Castberg (1846–1917), Norwegian painter and sculptor Peter Atke Castberg (1779–1823), Danish professor Peter Harboe Castberg (banker) (1844–1926), Norwegian banker Peter Hersleb Harboe Castberg (1794–1858), Norwegian priest and politician Torgrim Castberg (1874–1928), Norwegian violinist