The quake occurred at 8.29pm UAE time
There were no other injuries in the shooting, which took place at about 6am before the consulate was open for the day, said Officer Michael Lopez of the Los Angeles Police Department.
"Numerous rounds impacted the Chinese consulate," Lopez said.
Lopez said the man was discovered in his car dead from a self-inflicted gunshot wound.
The Chinese consulate, in a short statement, said it was extremely concerned about the incident and had asked the United States to take all necessary measures to protect the security of the building and diplomats working there.
China has also asked the United States to get to the bottom of what had happened, it added.
Authorities did not immediately identify the gunman and had few other details about the incident. Lopez said police did not typically release information about suicides.
In 2011 a naturalised US citizen originally from China was arrested after police said he opened fire at the same building with a handgun. There were no injuries in that incident.
The quake occurred at 8.29pm UAE time
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