Maxon studied at the Cooper Union between 1934 and 1938. He received his bachelor's degree from the University of Michigan in 1941. He attended Harvard University where he received his master's degree in 1945 and Ph.D. in 1948 on the subject of Tintoretto. That year he accepted a position as director of the University of Kansas Art Museum in Lawrence, KS. In 1952 he moved to be director of the art museum at the Rhode Island School of Design. In 1959 Maxon was appointed director of fine arts at the Art Institute of Chicago, replacing Daniel Catton Rich.