Federated Learning (FL) achieves great popularity in the Internet of Things (IoT) as a powerful interface to offer intelligent services to customers while maintaining data privacy. Under the orchestration of a server, edge devices (also called clients in FL) collaboratively train a global deep-learning model without sharing any local data. Nevertheless, the unequal training contributions among clients have made FL vulnerable, as clients with heavily biased datasets can easily compromise FL by sending malicious or heavily biased parameter updates. Furthermore, the resource shortage issue of the network also becomes a bottleneck. Due to overwhelming computation overheads generated by training deep-learning models on edge devices, and significant communication overheads for transmitting deep-learning models across the network, enormous amounts of resources are consumed in the FL process. This encompasses computation resources like energy and communication resources like bandwidth. To comprehensively address these challenges, in this paper, we present FLrce, an efficient FL framework with a relationship-based client selection and early-stopping strategy. FLrce accelerates the FL process by selecting clients with more significant effects, enabling the global model to converge to a high accuracy in fewer rounds. FLrce also leverages an early stopping mechanism that terminates FL in advance to save communication and computation resources. Experiment results show that, compared with existing efficient FL frameworks, FLrce improves the computation and communication efficiency by at least 30% and 43% respectively.