The victims were not immediately identified. Deputy Chief Kenneth Garner said the man killed his wife, an 8-year-old girl, twin 5-year-old daughters and twin 2-year-old sons. He then killed himself.
A revolver was found at the home.
"He was despondent, clearly, over his job situation," Garner said.
Either before or after killing his family, the man sent a two-page typewritten letter to KABC-TV, Garner said. The Burbank-based television station called police in that suburb, Garner said.
The TV station did not publicly release the note, but Garner described its content.
"Obviously he wanted somebody to find the bodies," Garner said.
"In the note, he clearly said he was going to kill himself, his wife and his kids," Garner said.
Garner said he didn't exactly know the man's job situation, but "it wasn't going well at work."
"Today our worst fear was realized," Garner said. "It's just not a solution. There's just so many ways you find alternatives to doing something so horrific and drastic as this."
The two-story home, much larger than its one-story neighbors, sits in front of a railroad track. A children's playset stood in the backyard and a pickup truck and sport utility vehicle were parked in the concrete front yard.
Wilmington, about 18 miles south of downtown, is a 10-square-mile community adjacent to the Port of Los Angeles.
(Copyright 2009 by The Associated Press. All Rights Reserved.)