An arrest warrant was issued for Desmond Moses, 55, after the shootings that killed a 30-year-old father and his 4-year-old son, the Los Angeles Times said.
The boy's 28-year-old mother was shot in both legs, her 7-year-old daughter was shot in the chest and a 6-year-old boy was shot in the pelvis. The mother and girl were in critical condition and the boy was in stable condition, the newspaper said.
An 8-year-old boy escaped injury.
"The father was found draped over two of the children, shielding them," Police Chief Mark Fronterotta said.
Authorities had not identified the victims but neighbors said the parents are Filimon and Gloria Lamas, the Times said.
Moses is suspected of shooting the family members in their home about 4 a.m. Saturday. Moses lived at a separate residence on the same property.
That house went up in flames after the shootings and firefighters discovered a body in the rubble, CNN reported. By early Sunday, officials hadn't confirmed the identity of the victim, but Inglewood Police Lt. James Madia said if it is Moses, the shootings have been solved.