Federated learning (FL) is an emerging collaborative machine learning method to train models on distributed datasets with privacy concerns. To properly incentivize data owners to contribute their efforts, Shapley Value (SV) is often adopted to fairly assess their contribution. However, the calculation of SV is time-consuming and computationally costly. In this paper, we propose FedCoin, a blockchain-based peer-to-peer payment system for FL to enable a feasible SV based profit distribution. In FedCoin, blockchain consensus entities calculate SVs and a new block is created based on the proof of Shapley (PoSap) protocol. It is in contrast to the popular BitCoin network where consensus entities "mine" new blocks by solving meaningless puzzles. Based on the computed SVs, a scheme for dividing the incentive payoffs among FL clients with nonrepudiation and tamper-resistance properties is proposed. Experimental results based on real-world data show that FedCoin can promote high-quality data from FL clients through accurately computing SVs with an upper bound on the computational resources required for reaching consensus. It opens opportunities for non-data owners to play a role in FL.