Greenland has adapted its justice system in the early 1950's to the aboriginal people that form the majority of its population. Given that Canada has imposed its own justice system to the Inuit living in Northern Canada, it is interesting to compare the two systems. In this paper, we first analyze the nature of each justice system in both jurisdictions. We then further explore how crimes are defined in each jurisdiction and come to the conclusion that the differences are not significant. We then proceed to review the court process and the sentences. It appears that the Greenland justice system tends to re-socialize the offender rather than to punish him/her as is the case in Canada. Finally, we conclude that it is possible to attempt to adapt the Canadian justice system to the Inuit in Nunavut following the Danish experience and propose a few ways of exploring Inuit customary law. The Greenland justice system is not perfect but is a good example of the possibility of adapting a justice system to an aboriginal population and may assist in showing where it works well and where it fails.