Sirhan Sirhan is currently serving a life sentence for killing Kennedy at the Ambassador Hotel in Los Angeles in 1968.
It's the latest of more than a dozen such hearings and the first in five years.
His attorney, William Pepper, said Sirhan doesn't even remember the night of the murder.
William Weisel, who was shot in the stomach during the assassination, said he wouldn't object to Sirhan's release if there is evidence there may have been a second shooter.
"I'm not an advocate for his release. I would not object to it if the parole board finds there is some credence in these new facts," said Weisel.
The board met at Pleasant Valley State Prison in Coalinga and evaluated whether Sirhan is a threat to himself or others and decided if he has accepted responsibility for the crime and expressed adequate remorse.
They also wanted to see if he has an adequate plan if he is released on parole.
Sirhan was last denied parole five years ago.
Pepper believes a second gunman shot Kennedy. He's also suggested that Sirhan was brainwashed.
The Associated Press contributed to this report.