In his long-shot appeal, Simpson argues his defence lawyer was ineffective.
The 65-year-old was convicted of the robbery of what he said were stolen articles of personal memorabilia.
Separately, Simpson was acquitted in 1995 of the murder of his former wife and her friend in Los Angeles.
The former National Football League running back is expected to testify during the five-day hearing, which began on Monday.
Simpson, who was shackled in court, is more than four years into a minimum nine-year to 33-year prison sentence.
In 2007, the former football player was accompanied by five other men as he tried to reclaim family pictures and footballs peddled by sport memorabilia dealers in a Las Vegas hotel room.
During the incident, two of Simpson's alleged co-conspirators carried guns.
Simpson says former defence lawyer, Yale Galanter, was ineffective at the subsequent trial because he had an personal interest in keeping private his own advice to Simpson.
Mr Galanter, according to Simpson, had repeatedly assured him that he could take back items related to his sporting career - items Simpson believed had been stolen - as long as no-one trespassed and no force was used.
The defence lawyer continued to conceal that he had been a witness to the crime, including during an appeal to a state court in 2010, Simpson says.
In a sworn statement outlining his planned testimony, Simpson says Mr Galanter "vigorously discouraged" him from testifying and never told him that prosecutors were willing to let him plead guilty to charges that would have brought a two-year minimum prison term.
"He consistently told me the state could not prove its case because I acted within my rights in retaking my own property," Simpson said.
Dr Norman Roitman, a Las Vegas psychiatrist, testified on Monday that Simpson's perception of what took place at the hotel room might have been muddled by football brain injuries as well as the effects of several vodka and cranberry juice cocktails.
"In those situations, people may focus on objects in front of them and be oblivious to other things," Mr Roitman said.
Appeals for a new trial because of ineffective counsel are seldom granted, but Simpson's history as a murder defendant in a widely-televised 1995 trial could affect the outcome, analysts say.
American football legend OJ Simpson has asked a Nevada judge to grant him a new trial in the 2008 armed robbery case that left him serving a lengthy prison sentence.