Kelly claims Verizon's "negligence" caused a "loss of civil liberties and freedoms," because he was convicted and sentenced to prison in connection with the case.
He is seeking $72 million in damages.
Kelly has a criminal history stretching back to 1985 when he was convicted of grand theft with a firearm and sentenced to 2 ½ years in prison.
Between 1985 and 2014, he was convicted at least 37 times on charges including rental property fraud, trafficking in stolen property, receiving money through fraudulent use of a credit card.
As of Monday, Verizon had not responded to the lawsuit.