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
The Duke and Duchess of Cambridge met young people who have battled mental health issues on Saturday.
Former Chancellor Lord Geoffrey Howe was Margaret Thatcher's longest-serving Cabinet minister, also taking on the role of Foreign Secretary.
Lord Geoffrey Howe is known by many for his resignation speech which was seen as the catalyst which destroyed Margaret Thatcher.