Police have arrested a Sydney man who allegedly killed a woman and baby before turning the gun on himself.

Key points:Police allege he shot the woman in the head at her home on Thursday before turning on himselfPolice say the man was known to the victim’s parentsPolice have arrested the alleged murderer at the address of the woman’s home in Melbourne’s eastEnding in police custody at the scene on Thursday night, the 31-year-old was taken to the Royal Melbourne Hospital where he died.

The woman was found with multiple gunshot wounds, a gunshot wound to the chest, and a wound to her right leg, a police spokeswoman said.

The 27-year the woman had lived with her parents for more than two years and the man lived with his parents for several years.

The mother had been in a relationship with the man’s parents for about four years.

Police allege the mother’s life had been threatened before the shooting.

“He was a known member of a street gang,” a police spokesman said.

“They had been involved in serious assaults on other people, including children.”

The woman’s life was threatened at the time of the incident.

“Police say they have been looking for the man since he turned himself in to police.

Anyone with information about the incident is asked to contact Crime Stoppers on 1800 333 000.