Griffith, 66, faces up to 10 years in prison, a $250,000 fine or both. He also may be ordered to pay restitution.
He will be sentenced in several months after a report is completed to guide U.S. District Judge Sharion Aycock with his punishment.
Griffith was indicted last April on two counts that he made false representations to the Social Security Administration to gain benefits intended for his stepdaughter, who lived the majority of the time with her biological father.
He was accused of taking in nearly $30,000 for which neither he nor the stepdaughter were entitled.
Without the plea deal, Griffith faces up to 15 years in prison.