A trial has begun for man accused of murdering his girlfriend and leaving her body to decompose in her apartment for up to 3-1/2 weeks.

Gordon Hieatt, 47, has pleaded not guilty in the High Court at Auckland to murdering Nuttidar Vaikaew, 48, in her Western Springs, Auckland, apartment some time after April 16 last year.

Crown prosecutor Rachel Reed told the jury Hieatt strangled Ms Vaikaew, a sex worker originally from Thailand, after an argument and left her body on a bed where police found it, covered with flies and maggots.

Police were contacted after Ms Vaikew's landlord stopped by to see if she was all right because he had not seen her for some time and because her rent was overdue.

Hieatt opened the door and introduced himself as Ms Vaikaew's boyfriend and told the landlord she was unwell.

But the landlord was concerned by a foul smell emanating from the apartment so he called the police, who went there to do a welfare check on May 12.

When they asked if everything was all right he said "no" and told them he and his girlfriend had been in an argument and he had killed her, Ms Reed said.

The curtains were drawn in the small apartment and there was a fan pointing at the bed where Ms Vaikaew's body lay.

"The smell was indescribable and putrid dead flies and maggots were all over the lounge and particularly on the bed," she said.

Ms Reed told the court Hieatt had visited another sex worker in Wellington after Ms Vaikaew's death, and also spent time in the apartment.

He also maintained a relationship with another woman in Thailand during this period. He told her about the killing via an online messaging service, Ms Reed said.

Ms Vaikaew immigrated to New Zealand from Thailand in 2001 and operated as a sex worker from the apartment.

She and Hieatt had been in an "on again off again" relationship for about 2-1/2 years.

The trial is expected to take about 2-1/2 weeks and the Crown will call 26 witnesses.