Terrance "Terry" Williams, 46, is scheduled to die by lethal injection on October 3rd.
Williams' lawyers plan to argue at Thursday's hearing that the prosecutor withheld evidence at the 1986 trial.
Williams lost a bid for clemency Monday before Pennsylvania's Pardons Board.
At that hearing, Williams' attorneys claimed he was sexually abused for years by the middle-aged man he admits beating to death in 1984 at the age of 18.
A unanimous vote was needed to recommend that Gov. Tom Corbett commute Williams' sentence to life imprisonment, but two of the five board members voted no.
None of the board members, who include state Attorney General Linda Kelly and Lt. Gov. Jim Cawley, commented after the vote. Kelly favored clemency and Cawley opposed it.
Philadelphia prosecutors described Williams as a violent, calculating criminal who had committed two robberies and another murder in a short period before he killed Norwood with a tire iron, the crime for which he was sentenced to death.
Tom Dolgenos, chief of federal litigation for the Philadelphia district attorney's office, said Williams initially sought to pin the murder on others and did not raise the issue of sexual abuse until 1998.
"The seriousness of the situation runs both ways," Dolgenos said.
In a statement, District Attorney R. Seth Williams said the allegations of sexual abuse are being made by friends and experts, not the convict himself, and that his death penalty has been upheld at all levels of the state and federal courts.
"The defendant has a long record of manipulative and malevolent behavior which eventually led to the deaths of two men," the city's top prosecutor said.
Pennsylvania has executed only three men since the death penalty was reinstated in 1976, and all of them chose to end their appeals. The most recent execution was in 1999. There are 200 people on death row in the state.