Proof of work (PoW), the most popular consensus mechanism for blockchain, requires ridiculously large amounts of energy but without any useful outcome beyond determining accounting rights among miners. To tackle the drawback of PoW, we propose a novel energy-recycling consensus algorithm, namely proof of federated learning (PoFL), where the energy originally wasted to solve difficult but meaningless puzzles in PoW is reinvested to federated learning. Federated learning and pooled-mining, a trend of PoW, have a natural fit in terms of organization structure. However, the separation between the data usufruct and ownership in blockchain lead to data privacy leakage in model training and verification, deviating from the original intention of federal learning. To address the challenge, a reverse game-based data trading mechanism and a privacy-preserving model verification mechanism are proposed. The former can guard against training data leakage while the latter verifies the accuracy of a trained model with privacy preservation of the task requester's test data as well as the pool's submitted model. To the best of our knowledge, our article is the first work to employ federal learning as the proof of work for blockchain. Extensive simulations based on synthetic and real-world data demonstrate the effectiveness and efficiency of our proposed mechanisms.