Maxwell Stewart Simpson was born September 11, 1896, in Elizabeth, New Jersey. In 1914, Simpson began his formal art studies in New York at the National Academy of Design School under Douglas Volk.  He also attended summer classes at the Art Students League in 1916.  In 1923, Simpson traveled to Paris and Italy, and in the spring of 1924 to Oxford England, where he stayed with a university professor while studying, painting portraits of the family's three children in exchange for board.

Upon his return to the United States, Simpson floundered for several years not satisfied with the realist style he had been painting and not fully accepting the avante-garde art of Europe that had flourished in America since the groundbreaking Armory Show in 1913.  After viewing a New York gallery exhibition in 1927, Simpson developed painting methods that would take on a new direction with the influences of George C. Ault, Ernest Fiene, Charles Demuth, and Yasuo Kuniyoshi.  Simpson had become one of New Jersey's foremost modernist painters and in 1959 was honored as "New Jersey Artist of the Year."

Simpson exhibited widely throughout his career including such venues as the Society Nationale de Beaux Arts, the Paris Salon in 1924, the Baltimore Museum of Art, the National Exhibition of American Art in 1937, the Corcoran Gallery of Art, the New York World's Fair, the Golden Gate Exposition in San Francisco, the National Gallery in Washington, the Carnegie Institute, the Summit Art Association, the Metropolitan Museum of Art, the American Artists For Victory, the Montclair Art Museum (Silver Medal, 1943) the Newark Museum, the National Academy of Design, the Los Angeles Museum of Art, the Terry Art Institute in Miami, the Art Institute of Chicago, the Whitney Museum of American Art, and the Silvermine Guild Association. Simpson also exhibited in New Hope with the Independents in 1934.

He was an instructor at the Elizabeth Art Club Studio from 1925 to 1928, and the Newark School of Fine and Industrial Arts from 1936 to 1946. He also conducted private classes at the Simpson Studio in Elizabeth, New Jersey.

Maxwell Stewart Simpson's work is in the collections of the Montclair Art Museum, the National Art Gallery in Washington, D.C.; the Newark Museum; the Shelburne Art Museum; and the Museum of the Briarcliff School in New York City.

For nearly fifty years, Maxwell Stewart Simpson lived in his carriage house studio in Scotch Plains, New Jersey.  It was there that he died in 1984, at eighty-eight years of age.