The family-run operation is the common governance model of Taiwanese enterprises. How to make sure the successor can succeed in succession is one of the most important issues in family enterprises. In this research, we applied analytic hierarchy processing (AHP) to determine the most critical personality traits that the successor should have. It can make encourage the successors to improve their personalities and abilities to be a qualified successor. The research results show that the personality trait of the successor is the most concerned issue of most business owners, followed by the ability of the successor and other factors. The results of this research can be provided to the family business as a reference in the face of the choice of successors.