The jury in Grace Millane's murder trial have been shown CCTV of the alleged killer transporting a suitcase containing Grace's body. 

Crown prosecutors allege that on the night of December 1 last year - the eve of Miss Millane's 22nd birthday - the accused, 27, strangled the young Brit to death in his central city apartment after the pair spent the night drinking.

He then stuffed Miss Millane's body into a suitcase and dumped it in a shallow grave amongst some bush in Auckland's Waitākere Ranges.

In the latest day of the trial, jurors saw how CCTV captured her date, a 27-year-old man who cannot be named for legal reasons, buying a suitcase and a shovel before moving her body in a red Toyota hatchback.

He had rented the vehicle the day she died.

CCTV showed defendant wheeling a luggage trolley into a lift at the CityLife hotel in central Auckland.

He returned with the trolley carrying two suitcases, one of which he has since admitted contained Miss Millane's body.

Jurors were also shown images of the moment detectives found the suitcase with Miss Millane's body inside buried in a wooded area outside Auckland.

The court also heard from a former journalist who the defendant went on a date with during the day he was disposing of Miss Millane's body.

She told how, during small talk, he calmly recounted a story of a man who had accidentally killed a woman during sex and had been prosecuted.

"It's crazy how guys can make one wrong move and go to jail for the rest of their life", she says he told her.