A man has pleaded guilty to the murder of a woman with Down syndrome, Lena Zhang Harrap.

Today at the High Court in Auckland, family members filled the public gallery and tears were shed as Shamal Shamar entered guilty pleas over Harrap's death last year.

Shamar was expected to stand trial next month for Harrap's murder, sexual violation and for driving a motor vehicle in a dangerous manner.

Harrap vanished while on her daily walk on September 22, 2021, in Mt Albert.

Her body was discovered hours later along a bush-lined walkway, about a kilometre from her home.

The 27-year-old was active in StarJam, a non-profit organisation that gives those with disabilities an opportunity to perform.

"Lena may have been small in stature but she had the biggest heart," Lynfield College principal Cath Knell said last year.

"Her wicked sense of humour backed up by a mischievous smile brought much joy to those who taught her."

Prosecutor Matthew Nathan said the Crown would be seeking a sentence of preventive detention on Shamar's sexual violation charge.

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In December last year, Justice Fitzgerald found Shamar fit to stand trial after reviewing two psychiatrist and psychologist reports.

His lawyer Jonathan Hudson, originally entered not-guilty pleas on his client's behalf and sought to order two other reports to address the defendant's mental health.

The 31-year-old, listed in court documents as having no fixed address, was arrested on September 24 after he was found in a vehicle in Papatoetoe.

Justice Sally Fitzgerald acknowledged Harrap's family and friends in court.

Shamar will appear for sentencing on March 30 next year.

He faces a maximum 20 years in prison for sexual violation and a life sentence for the murder.

- Ellen Thompson, Open Justice