Circuit Judge Debra S. Nelson agreed Friday to the request by defense attorney Mark O'Mara, the Orlando Sentinel reported.
Zimmerman is charged with second-degree murder in the death of Martin, who was 17 when Zimmerman shot and killed him in Sanford, Fla. O'Mara wants to show that Martin had been in trouble at school and participated in mixed martial arts.
Zimmerman says he shot the unarmed teenager in self defense.
Nelson said Martin's school records won't be released to the media, and jurors won't see them unless she believes they are relevant.
Martin's parents protested the defense request in a news conference 2 hours before the hearing began. His father, Tracy Martin, said it was wrong "to make a dead child seem as if they're the perpetrator."
The judge ruled against a prosecution request to seal defense subpoenas or hold closed door meetings about them. She also decided the state could see Zimmerman's medical records, but only after she looked at them.
Nelson further agreed to a defense request for the telephone records of a 16-year-old girl who was talking to Trayvon by cellphone when he was shot.