[1] On August 15, 1986, Graham was nominated by President Ronald Reagan to a seat on the United States District Court for the Southern District of Ohio vacated by Judge Robert Morton Duncan.

Graham was confirmed by the United States Senate on September 25, 1986, and received his commission the following day.

He served as chief judge from 2003 to 2004, assuming senior status on August 31, 2004.

[1] Like many district judges on senior status, Graham occasionally serves with the court of appeals on a rotating basis.

While serving with the Sixth Circuit, he supplied a dissenting opinion on a decision upholding the Patient Protection and Affordable Care Act mandate to purchase health insurance.