Nowadays, federated recommendation technology is rapidly evolving to help multiple organisations share data and train models while meeting user privacy, data security and government regulatory requirements. However, federated recommendation increases customer system costs such as power, computational and communication resources. Besides, federated recommendation systems are also susceptible to model attacks and data poisoning by participating malicious clients. Therefore, most customers are unwilling to participate in federated recommendation without any incentive. To address these problems, we propose a blockchain-based federated recommendation system with incentive mechanism to promote more trustworthy, secure, and efficient federated recommendation service. First, we construct a federated recommendation system based on NeuMF and FedAvg. Then we introduce a reverse auction mechanism to select optimal clients that can maximize the social surplus. Finally, we employ blockchain for on-chain evidence storage of models to ensure the safety of the federated recommendation system. The experimental results show that our proposed incentive mechanism can attract clients with superior training data to engage in the federal recommendation at a lower cost, which can increase the economic benefit of federal recommendation by 54.9\% while improve the recommendation performance. Thus our work provides theoretical and technological support for the construction of a harmonious and healthy ecological environment for the application of federal recommendation.