Extra-contractual liability is an important institution recognized in the civil codes of many countries, including the French Republic and Vietnam. It is the obligation to repair the damage that one causes to a third party. Or, it can be defined as the obligation imposed on a person to repair damage suffered by another person. However, in certain cases which are provided for by law, the victim of the damage will not be compensated, for example: force majeure, the fault of the victim, the victim does not apply the necessary and reasonable measures to prevent and limit the damage, etc. This article presents and analyzes the provision relating to the obligation to limit the damages of the victim, within the extra contractual liability, which interests us, in the Vietnamese and French laws in a broad way, that is to say in s relying on the texts of laws, case law and doctrine. This is a new provision, it is derived from British law (the theory of mitigation of damages), and is recognized in the Civil Code of Vietnam since 2015. Meanwhile, in France, in addition to efforts lawyers in the recognition of this provision in French law in the program of legislative reform, this question still comes up against many contradictory points of view. Through this article, the author wishes to contribute to bringing multidimensional perspectives related to the obligation to limit the damages of the victim in extra contractual liability, and at the same time to propose some solutions concerning the types of damage for which the victim is obliged to limit, necessary and reasonable measures, the costs or damages incurred by the victim in order to minimize his damage in order to contribute to the improvement of Vietnam's legal regulations on this issue.