McGraw began his career in 1994 as a correctional officer at Eastern Kentucky Correctional Complex (EKCC) in West Liberty. He was promoted to the position of sergeant in 2000 and then to coordinator in 2004. He transferred to LSCC upon the facility's opening in 2005 as a unit administrator I. He then transferred to a training coordinator's position at LSCC in 2007, holding that position until he transferred to captain II in 2014. McGraw served as the Corrections Emergency Response Team (CERT) commander for LSCC from 2005 until 2014 when he became the Eastern Region CERT commander.
During his 20-year career, McGraw has been recognized with numerous awards including the 2013 Commissioner's Award. He is a 2013 graduate of the Commissioner's Executive Leadership Program and an active member of Kentucky Council on Crime and Delinquency (KCCD). McGraw also serves as the current KCCD Laurel Gorge chapter president and a 2010-11 past president.