They say Clarence Newcomb was arrested Friday at the home he shared with 82-year-old Kathleen Newcomb in Kings Park, on Long Island 40 miles east of New York City.
Suffolk County police say a man called them at about 4:35 a.m. to report the woman was lying on the floor. Officers say they found her dead.
Medical officials haven't determined how she died. No weapons have been recovered.
Police say the 25-year-old Clarence Newcomb told them he and his grandmother had argued over what to watch on TV. Lt. Jack Fitzpatrick says he doesn't know what shows were involved.
Newcomb is in police custody and can't be reached for comment. Police say he's unemployed, and it's unclear if he has an attorney. He faces arraignment Saturday.