A possessive man who could not accept that his girlfriend was seeing other men - despite an agreement to have an open relationship - has been sentenced to 13 years' jail for killing her during a quarrel.

Neo Chun Zheng, 29, who stabbed Ms Soh Yuan Lin, 23, once in the neck outside his Boon Lay flat on Nov 26, 2015, told the High Court on Monday that words could not express his "eternal regret".

"I have completely failed her and I can never forgive myself for all that had happened. It was a toxic relationship but this would not take away my love for her," he said, reading from a note before sentencing.

Neo also apologised to Ms Soh's family. "I am very very sorry for causing you such tremendous grief, sorrow and suffering... I can only hope that some day, you may find it in your heart to forgive me."

It was revealed in court that Ms Soh's family had rejected his apology letter after he pleaded guilty to a charge of culpable homicide in October last year.

In sentencing, Judicial Commissioner Pang Khang Chau found there was enough evidence of Neo's remorse from his police statements. He imposed a 13-year sentence after considering precedents.

Neo and Ms Soh, a former air stewardess, met when they started work at the Marina Bay Sands casino in April 2014. They began dating but Ms Soh wanted the relationship to be "non-exclusive" and kept secret. Neo agreed, but still felt she was cheating on him whenever she saw other men.

In September 2015, they quarrelled after he discovered that she was texting someone she had kissed at a club. She broke up with him later that month as she felt he was too possessive.

Neo later found out that Ms Soh was using the dating app Tinder and told a friend he thought about disfiguring her with acid. He continued telling her she had hurt him and she had to make it up by buying meals for him or going out with him.

On Nov 25, 2015, when Ms Soh went to Neo's flat to deliver a packet of food, they began quarrelling. Neo's mother told him to let her leave, but he went to his room and got a folding knife. When Ms Soh tried to wrest it away, Neo pushed her away and stabbed her once in the neck. He gave himself up when the police arrived. Ms Soh was pronounced dead three hours later in hospital.

On Monday, Deputy Public Prosecutor Wong Kok Weng sought 15 years' jail. But Neo's lawyer Tan Jun Yin asked for not more than 10 years.