They say the nine-time Olympic medalist hasn't lived in New Jersey for the required four years. They say he has lived and voted in California until recently.
Lewis says he owns two homes in New Jersey, including one in Medford that was purchased in 2005.
The former track star says he transferred his voter registration last Monday, the same day he officially declared his candidacy as a Democrat in the state's 8th District.
The 49-year-old political novice grew up in Willingboro, N.J.
The GOP complaint to New Jersey Secretary of State Kim Guadagno asks that Lewis' name be pulled from the primary ballot.
A response from Lewis's attorneys is expected later Monday.