Richard Simpson may refer to:

• 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 director
• Rik Simpson, British record producer, musician and songwriter