The first shooting happened about 4 a.m. along the 1100 block of North West Street in Anaheim.
The second shooting happened at about 5:30 a.m. approximately 28 miles northwest in Koreatown.
Police responded to the first incident and found a man in his 50s shot at an apartment building. He was rushed to the hospital, where he later died.
An hour later, Los Angeles police responded to a fight at a home in Koreatown and found a man shot in the head inside a home at 1128 S. Irolo St. The second victim remains in critical condition.
After shooting the second victim, the suspect turned his gun on himself and took his own life, police said.
Officials believe the shootings may be connected.
The names of the deceased were not immediately released.
The Associated Press contributed to this report.