Richard Simpson is the name of:
- Richard Simpson (martyr) (c. 1553–1588), English Catholic priest, martyred during the reign of Elizabeth I
- Richard Simpson (writer) (1820–1876), Catholic writer and literary scholar
- Richard F. Simpson (1798–1882), U.S. Representative from South Carolina
- Richard M. Simpson (1900–1960), U.S. Representative from Pennsylvania
- Richard Simpson (Scottish politician) (born 1942), Scottish politician
- Dick Simpson (born 1943), American baseball outfielder
- Dick Simpson (politician) (born 1940), former Chicago alderman
- Chubb Rock (Richard Simpson, born 1968), New York-based rapper
- Richard Simpson (rugby union) (c. 1885–?, rugby union player who represented Australia
- Richard J. Simpson, professor of biochemistry
- Richard James Simpson (born 1967), American singer and guitarist
- Rick Simpson, American set decorator
- Rik Simpson, British record producer, musician and songwriter