Peter Madsen, 47, was sentenced to life in prison in April for murdering and torturing Ms Wall, 30, while she was aboard his privately built submarine.
In a three-day hearing, he will not dispute the guilty verdict, but seek a time-limited rather than open-ended prison sentence. The average life sentence in Denmark is 16 years.
The disappearance of Ms Wall last June, and the details of her killing that subsequently emerged, horrified people in Denmark and across the globe.
Image: Madsen admitted dismembering Kim Wall's body
Madsen was convicted of torturing and sexually assaulting the young journalist, who had boarded his ship to report a story, before murdering her and dismembering her body.
Parts of the 30-year-old‘s body were found in various locations on the Copenhagen coast, many scarred with multiple stab wounds and strapped with pieces of heavy metal to ensure they would sink.
Although the Danish inventor admitted dismembering Ms Wall‘s body, he has insisted that she died accidentally aboard his submarine.
Madsen‘s shifting explanations and apparent lack of remorse prompted the court to label him as having “psychopathic tendencies” as it ruled the murder was sexually motivated and premeditated.
Mr Madsen appeared in a dark blazer, suit and jeans in the appeal hearing on Wednesday, and listened as his lawyer Betina Hald Engmark read his previous statements.
“My client is not satisfied with the (life) sentence. that‘s why we are here, not to find out whether he is guilty or not,” she said.
Ms Wall was a respected freelance journalist, who had reported from China, Uganda and Haiti for a wide range of publications, on topics including feminism and voodoo.
A memorial fund has been established in her name.