The wide spread of a false rumor could cause huge losses. Isolating some rumor spreaders is an effective approach to limiting the spread of the rumor, at the cost of violating human rights. This paper focuses on developing an isolation–conversion strategy to minimize the impact of the rumor. Based on a novel rumor–truth mixed spreading model, we measure the impact of the rumor. On this basis, we model the isolation–conversion problem as an optimal control problem. We show that the optimal control problem admits an optimal control, and we present the optimality system for solving the optimal control problem. We give some optimal isolation–conversion strategies by solving the corresponding optimality systems. To our knowledge, this is the first time the isolation–conversion problem is treated in this way.