"There are 19 issues here in our writ and all you need is one of them to be granted and Mr. Simpson gets a new trial," Fumo said. "It just seems overwhelming that more than one of them should or would be granted and I'm confident he'll get a new trial."
Simpson is serving a 33-year prison term and is eligible for parole in 2017.
Simpson lost an appeal of his verdict in 2010 in Nevada Supreme Court. Prosecutors say there is no evidence of conflict of interest and Simpson's claims are "without merit."
Simpson, who played in the NFL from 1969 to 1979, was acquitted in a criminal trial in the 1994 deaths of his ex-wife, Nicole Brown Simpson, and her friend, Ronald Goldman. A civil jury later slapped him with a $33 million wrongful-death judgment.