A suspected gunman was arrested by Los Angeles police after barricading himself inside a shop full of people and killing one woman.

The suspect, a 28-year-old, gave himself up after crisis negotiations with police, the LAPD said.

The man is understood have shot his own grandmother and girlfriend before fleeing, prompting a high-speed chase in which he fired shots at police pursuing him. He then crashed the car and entered the Trader Joe’s store.

Aerial footage from local TV stations NBC Los Angeles and CBS Los Angeles showed people leaving a store window using a rope ladder and police carrying children to safety through a parking lot in the city's Silver Lake neighbourhood.

The suspect released some of the hostages himself before eventually agreeing to give himself up to police. Mayor Eric Garcetti subsequently said that a woman had been killed in the incident. She has not been identified.

Police cordoned off the area. Photo: Reuters

Trader Joe employees and patrons wait outside as the hostage situation unfolds. Photo: Reuters