According to KTLA, the Gardena Police Department said the incident happened at 10 pm at the Target store on Redondo Beach.
At that time, the two men quarreled, then brawled inside this store.
One person pulled out a gun and shot the other two times, then ran away, the police station said.
Law enforcement officials said the person who was shot was taken to a local hospital, but it was not clear how his condition was.
Police were looking for the shooter in Target, saying the suspect was 5 feet 7 inches to 5 feet 10 inches tall, had dark hair and was dressed in dark clothing.
However, the Gardena Police Department did not know what caused the two sides to quarrel, which ultimately led to the shooting.