The current research on federated learning has focused on federated optimization, improving efficiency and effectiveness, preserving privacy, etc., but there are relatively few studies on incentive mechanisms. Most studies do not take into account the fact that if there is no profit, the participant is not motivated to provide data and train the model, and the task requester has no way to identify and select reliable participants with high-quality data. Therefore, in this paper, we propose an incentive mechanism for federated learning based on reputation and reverse auction theory. Participants bid for tasks, and reputation indirectly reflects their reliability and data quality. In this federated learning scenario, we select and reward participants by combining their reputation and bid price under limited budget conditions. Theoretical analysis proves that this mechanism meets properties such as truthfulness, etc., and simulation results show the effectiveness of it.