Police closed off the area and warned residents to stay inside their homes until they could be escorted out.
The SWAT team worked late into the night Sunday in their search for the gunman.
"We don't know where he's at," said Sgt. Jeremiah Hart of the Torrance Police Department. "We think he's inside the apartment complex somewhere but whether he's inside a laundry room or inside an apartment, we're not sure."
Authorities said they don't know whether the gunman is dead or alive. Police attempts to reach the man had been unsuccessful.
According to police, the suspect was well armed when he shot his neighbor. He took about 16 to 18 shots.
"It just makes it so dangerous because he could have an arsenal inside his apartment or he could have just one hand gun," Hart said. "That's why we're using the SWAT team to do it as safely as possible."
Several neighbors said they heard the gunshots ring out.
"We heard these loud noises, about seven of them and then a pause, six or seven more after, then one loud last one," said neighbor Sarah Richard. "It was pretty loud."
Neighbors said the gunman and the victim, who lived below him, had an ongoing dispute over loud music and noise.
"He was kind of a loner, kind of a quiet guy," said Christine Lee, another neighbor. "He kept to himself, but there had been some problems in the past."
The suspect is described as a middle-aged Hispanic male.
The victim is described by neighbors as a 39-year-old father of two boys who would often stay with him on the weekends. The children were not there Sunday.
CNS contributed to this report.