Christopher Dorner was shot at by a fish and game ranger, as he fled in a stolen vehicle in north-east Los Angeles, Reuters is reporting.
The agency states that earlier Dorner had broken into a home, tied up a couple and stole their pick-up truck.
Local media is also reporting it is believed one of the hostages was able to flee and raise the alarm.
More top news
A hacker group who claimed to be behind a cyber attack on Sony Pictures have posted a message online apparently mocking the FBI.
The returns of Benedict Cumberbatch's detective and the X Factor judge were among 2014's most tweeted TV moments in a billion conversations.
A family has issued an appeal to help find their missing pet turkey - in case he gets gobbled up as someone's Christmas dinner.