A jury handed down the verdict in the Supreme Court in Melbourne just before 1pm on Thursday.

The trial started last month, after Adam Margolis, 40, pleaded not guilty to murdering 26-year-old Mai-Yia Vang in his Butler Street home sometime on February 24 and February 25, 2018.

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The court heard Margolis and Ms Vang formed a relationship in January 2018 after they met through an online chat service.

Ms Vang then moved in with Margolis at his California Gully home on February 18 that year.

In the week leading up to Ms Vang's death, the court heard the couple had arguments about Ms Vang's apparent contact with an ex-partner.

After a "heated argument" late on February 24 or in the early hours of February 25, Margolis choked or strangled Ms Vang until she died.

He then made plans to kill himself and wrote a 12-page email explaining why he killed Ms Vang.

Margolis sent the email to three associates, one of whom received the email several hours later and contacted police.

Police arrived at Margolis' address in the early hours of February 27 to find Margolis lying on a mattress in his bedroom. The court heard he appeared to be having a drug overdose.

Ms Vang's dead body was found in a different room.

An autopsy report said there was male DNA on Ms Vang's neck and under her fingernails, which was likely to have come from Margolis.

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Crown prosecutor Mark Rochford QC told the jury the email Margolis sent following Ms Vang's death confirmed he consciously, deliberately, and voluntarily killed her.

Mr Rochford said Margolis' email made him guilty of murder and the 40-year-old's decision to give evidence in the trial was his way of "getting away from the consequences".

The crown prosecutor said while Margolis told the court he "overstated his culpability" in the email, that was a "vastly different" sentiment to unconsciously killing a woman.

Defence counsel Bruce Walmsley QC said it was conceded there were "major inconsistencies" between the email and Mr Margolis' evidence.

But Mr Walmsley said jurors needed to put the email in the context of the situation.

Mr Walmsley said it was an "extraordinarily difficult time" for Mr Margolis and he wrote the email believing he would later kill himself.

The defence lawyer said while the email was "bizarre and weird in the extreme", Mr Margolis' sworn evidence came across as "sober and solemn".

Margolis was remanded in custody and is due to return to the Supreme Court in April for a plea hearing.

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