A murder trial has heard how a man who allegedly murdered his fiancée had prevented her from leaving him days before she died.

Simon Gittany, 39, has been charged with throwing his 30-year-old fiancée Lisa Harnum over the 15th-storey balcony of their Sydney CBD apartment in July 2011.

The Crown alleges he was extremely possessive and controlling to the point where she lost her friends and regular contact with her family in Canada.

The Supreme Court in Darlinghurst heard Gittany tracked Ms Harnum's movements, texts, emails and phone calls and had cameras set up in their apartment.

The Crown alleges that just days before she died, Ms Harnum knocked on her neighbour's door begging for help and was then dragged into their apartment by the accused.

The Crown alleges Gittany threw her Ms Harnum to her death, and one witness reported seeing the accused punch the air afterwards.

Gittany's lawyer Philip Strickland, SC, argues Ms Harnum went over the railing of their balcony and Gittany tried to help her, but she fell to her death.

He told the court although her motive for going over the balcony was unknown, it may have been suicide or a cry for attention.

Defence says Ms Harnum was conflicted and confused

The defence argues her state of mind is critical, saying she was conflicted and confused and suffered from low self-esteem.

The trial heard Ms Harnum pleaded with her mother, who lives in Canada, to come and help her.

Marjory Joan Harnum told the Supreme Court that her daughter told her Gittany had pushed her into a planter and then down some stairs.

Marjory Harnum said she called her daughter during an argument with Gittany, and she said 'mummy, you've got to come and help me', before her phone went dead.

Ms Harnum also told her mother she had to be careful about what she said in text messages, as Gittany read them.

In other text messages she said he was a walking time bomb, she felt trapped and wanted to move to Melbourne.