Federated learning, as a promising machine learning approach, has emerged to leverage a distributed personalized dataset from a number of nodes, e.g., mobile devices, to improve performance while simultaneously providing privacy preservation for mobile users. In the federated learning, training data is widely distributed and maintained on the mobile devices as workers. A central aggregator updates a global model by collecting local updates from mobile devices using their local training data to train the global model in each iteration. However, unreliable data may be uploaded by the mobile devices (i.e., workers), leading to frauds in tasks of federated learning. The workers may perform unreliable updates intentionally, e.g., the data poisoning attack, or unintentionally, e.g., low-quality data caused by energy constraints or high-speed mobility. Therefore, finding out trusted and reliable workers in federated learning tasks becomes critical. In this article, the concept of reputation is introduced as a metric. Based on this metric, a reliable worker selection scheme is proposed for federated learning tasks. Consortium blockchain is leveraged as a decentralized approach for achieving efficient reputation management of the workers without repudiation and tampering. By numerical analysis, the proposed approach is demonstrated to improve the reliability of federated learning tasks in mobile networks.