The decomposed bodies of a man and woman were found early Saturday morning in a trash bin at a home on Lassen Street near Oso Avenue.
The suspect, 43-year-old Brent D. Zubek, is a father of three and lives at the residence.
Police have not released the identities of the victims and they're not saying how they died. Officials are not commenting on Zubek's relationship with the two victims.
The murders may have occurred at a different location than where the bodies were discovered, according to investigators.
Authorities are asking the public for help in finding Zubek.
"No information is too small," said Los Angeles Police Capt. Maureen Ryan. "If you think you see him, call. We have our tipline manned."
Zubek's sister said the family is in shock that her brother is a suspect in the double-murder. She said she doesn't believe her brother is capable of murder, but that he should turn himself in.
"I talked to him, you know, as frequently as possible. It's been several weeks now that I haven't," Lisa Zubek said. "This is very much out of the blue.
"I definitely want him to turn himself in, because I would like for him to -- I don't want this to go horribly wrong," she said.
Detectives spotted the suspect's black Ford F-150 pickup truck parked on Sepulveda Boulevard in North Hills Sunday.
When he drove away, undercover officers followed him, but he managed to evade police and later abandoned the truck at a parking lot in Sherman Oaks.
Zubek was described as white, about 5 feet 11 inches tall, weighing 185 pounds. He has short brown hair and blue eyes.
The L.A. County Coroner's Office will be performing an autopsy on the bodies on Monday.
Anyone with information about Zubek's whereabouts was asked to call the Los Angeles Police Department at (877) 527-3247.