No hostages were seriously hurt.
He had crashed a vehicle nearby after firing multiple rounds at officers pursuing him, police said.
Meanwhile, as the suspect entered the store, employees and customers inside scrambled for cover.
Lopez said it's unclear whether there are hostages inside of the Trader Joe's, but footage from news helicopters shows police officers helping people from the store.
Law enforcement sources told The Times that the gunman opened fire on officers and then ran inside the store.
Coroner's officials identified the woman Sunday as 27-year-old Melyda Corado. Police said he had a wound to his arm.
As the standoff continued, the suspect held people hostage and made demands with crisis negotiators.
A police chase ensued and finally came to an end when the suspect hit a power pole outside the Trader Joe's on Hyperion Avenue at Griffith Park Boulevard.
LAPD said a SWAT team was in place.
"Then this guy comes out of the auto and starts running toward TJs", 91-year-old witness Don Kohles told CNN, referring to the grocery store.
Christian Dunlop, a real estate agent and actor who lives nearby, said he was watching from the corner when he saw four people flee out the front of the store.
A mother in Montana recalled moments of panic as she watched the Silver Lake Trader Joe's hostage situation unfold while her daughter hid inside the store.
Among the injured was a 20-year-old woman, who was removed from a vehicle, Stewart said. Some were able to escape when a store employee activated an emergency ladder out of a second floor store window. Among them was a police officer carrying a small child, he said.
A TraderJoe's employee is comforted after a suspect barricaded inside the supermarket in Silverlake, Los Angeles, on July 21, 2018.
The suspect had a pistol in his hand and "just started opening fire on the police behind him", Field said. "She had heard the gunshots", Felt said.
"Duck down! Duck down!" an officer shouted at her. Officers escorted the girlfriend from the vehicle. At about the same time, other officers went into the store and rushed out Kolhes and others near him.
The suspect ran into the store and immediately barricaded himself with as many hostages as he could bunch together, standoff that lasted a full three hour period.
Investigators are not sure what led to the initial violence that produced the auto chase and standoff.
Police believe a man involved in a standoff with officers at a Los Angeles supermarket shot his grandmother and girlfriend before firing at officers during a pursuit, then crashing outside the supermarket and. Atkins' grandmother was hospitalized in critical condition on Sunday.
LAPD spokesman Mike Lopez said the suspect had fired at officers multiple times as he fled the original shooting in the south of the city earlier on Saturday afternoon.
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