An Auckland computer programmer strangled his girlfriend to death then lived with her decomposing body for nearly a month, a court has been told.

Gordon Hieatt, 48, is accused of murdering his "on-again, off again" girlfriend Nuttidar Vaikaew, 48, between April 17 and May 12 this year.

Thai national Ms Vaikaew, known as "Sky", worked as a prostitute out of her flat in Warwick Street, Western Springs prior to her death. The court heard that Hieatt had moved in with her several months before the incident.

At a depositions hearing at the Auckland District Court this morning prosecutor Rachael Reed said the accused had killed his girlfriend after having an argument with her in early April.

Ms Vaikaew had not been seen by neighbours or her landlord for nearly a month and so on the afternoon of May 12 her landlord, Ray Goffin, went to visit her home.

After knocking several times on the door of Ms Vaikaew's flat, Hieatt answered the door and said to Mr Goffin, "I am Gordon, Nuttidar's boyfriend, Nuttidar is sick and she has been sick for a few days".

Mr Goffin became suspicious and rang police, Ms Reed told the court.

When police arrived at the home and enquired after Ms Vaikaew, Hieatt answered the door and told them: "She's dead and has been dead for four weeks. We had an argument and I killed her," the court heard.

Police discovered her body in the bed in the lounge room, covered by sheets and bedding, Ms Reed said.

Later Hieatt told police he had "choked" Ms Vaikaew on April 17. "He said they had an argument and it got out of hand," Ms Reed said.

The police will call nine witnesses over the two-day depositions hearing.