As a distributed machine learning paradigm, federated learning (FL) enables participating clients to share only model gradients instead of local data and achieves the secure sharing of private data. However, the lack of clients’ willingness to participate in FL and the malicious influence of unreliable clients both seriously degrade the performance of FL. The current research on the incentive mechanism of FL lacks the accurate assessment of clients’ truthfulness and reliability, and the incentive mechanism based on untruthful and unreliable clients is unreliable and inefficient. To solve this problem, we propose an incentive mechanism based on the reputation mechanism and reverse auction to achieve a more truthful, more reliable, and more efficient FL. First, we introduce the reputation mechanism to measure clients’ truthfulness and reliability through multiple reputation evaluations and design a reliable client selection scheme. Then the reverse auction is introduced to select the optimal clients that maximize the social surplus while satisfying individual rationality, incentive compatibility, and weak budget balance. Extensive experimental results demonstrate that this incentive mechanism can motivate more clients with high-quality data and high reputations to participate in FL with less cost, which increases the FL tasks’ economic benefit by 31% and improves the accuracy from 0.9356 to 0.9813, and then promote the efficient and stable development of the FL service trading market.