Federated learning is a novel machine learning framework that enables multiple devices to collaboratively train high-performance models while preserving data privacy. Federated learning is a kind of crowdsourcing computing, where a task publisher shares profit with workers to utilize their data and computing resources. Intuitively, devices have no interest to participate in training without rewards that match their expended resources. In addition, guarding against malicious workers is also essential because they may upload meaningless updates to get undeserving rewards or damage the global model. In order to effectively solve these problems, we propose FIFL, a fair incentive mechanism for federated learning. FIFL rewards workers fairly to attract reliable and efficient ones while punishing and eliminating the malicious ones based on a dynamic real-time worker assessment mechanism. We evaluate the effectiveness of FIFL through theoretical analysis and comprehensive experiments. The evaluation results show that FIFL fairly distributes rewards according to workers' behaviour and quality. FIFL increases the system revenue by 0.2% to 3.4% in reliable federations compared with baselines. In the unreliable scenario containing attackers which destroy the model's performance, the system revenue of FIFL outperforms the baselines by more than 46.7%.