Born in Ardmore, Oklahoma in 1916, J. Press Maxwell was born into a family well-known for golf course architecture. His father, Perry Maxwell, was highly-regarded in the golf architecture world. Following the footsteps of his father, Maxwell after school would apprentice with his father. As a young man, he would help out his father in the building of famous layout Southern Hills in Tulsa, Oklahoma, during the Depression.

After serving in World War II and having to take care of his father while in poor health, Maxwell began doing his own design work. He was known as an architect for his well-contoured, challenging greens. His ability to create sophisticated green structures lead him to do green remodeling at courses like Pine Valley Golf Club and Augusta National.

Maxwell was elected into ASGCA in 1953 and served as ASGCA President from 1960-1961