Andriessen is a Dutch patronymic surname meaning son of Andries cognate to the surname Andrews. People named Andriessen or Andriesse include:
Anthonie Andriessen (1746–1813), Dutch painter
Cees Andriessen (b. 1940), Dutch painter and sculptor
Cornelis Dirk Andriesse (born 1939), Dutch physicist
Emmy Andriesse (1914–1953), Dutch photographer
Frans Andriessen (b. 1929), Dutch politician
nl:Gijs Andriessen (b. 1957), Dutch videoartist/composer, son of Jurriaan Andriessen
Hendrick Andriessen (1607–1655), Flemish painter
Hendrik Andriessen (1892–1981), Dutch composer, brother of Willem and Mari
Jurriaan Andriessen (composer) (1925–1996), Dutch composer, son of Hendrik Andriessen
Jurriaan Andriessen (artist) (1742–1819), Dutch decorative painter
Koos Andriessen (b. 1928), Dutch politician
Louis Andriessen (b. 1939), Dutch composer, son of Hendrik Andriessen
Mari Andriessen (1897–1977), Dutch sculptor, brother of Willem and Hendrik
Willem Andriessen (1887–1964), Dutch pianist and composer, brother of Hendrik and Mari
Purely patronymic:
Albert Andriessen Bradt (1607-1687), Norwegian-born settler from Amsterdam in New Amsterdam