This research is an empirical study that analyzes the relationship of trust between an incumbent CEO and a successor during succession in a family business. We use the relationship of trust between an incumbent CEO and a successor as a mediating variable. A successor’s conversational ability, home environment, and involvement of family members are used as independent variables. A successor’s willingness to succeed is used as a dependent variable. Before analyzing the main research model, we conducted the first analysis to find the influence on the successor’s willingness to succeed, and the relationship of trust had the greatest effect among the independent variables. As a result of the main research model, it was found that the successor's conversational ability and home environment affected the relationship of trust, but the involvement of family members was not. Besides, the relationship of trust was found to have a fully mediating effect between a successor's conversational ability, home environment, and a successor’s willingness to succeed. This study can be said to be meaningful in that it discovered a variable called home environment that was not mainly dealt with in the business research field and reaffirmed the importance of the relationship of trust between them.