After graduating from the Wyoming County public school system, McGraw attended Morris Harvey College (now the University of Charleston) where he earned his Artium Baccalaureus in 1960.
[citation needed] After his service in the West Virginia Legislature, McGraw returned to Wyoming County to practice law where he was elected to the Board of Education in 1986 and later as Prosecuting Attorney in 1996.
In 1998 McGraw successfully campaigned for an unexpired six-year term in the Supreme Court of Appeals of West Virginia.
Afterwards, McGraw filed a lawsuit against Charleston attorney George Carenbauer and West Virginia Media Holdings over a campaign ad which McGraw claimed portrayed his speech during the 2004 United Mine Workers of America's Labor Day rally in Racine, West Virginia in an unfair light.
[6] In 2008 and 2016 McGraw successfully ran for a Circuit Court Judge post which he won both times and received over 80 percent of the vote.