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It has been proved by recent works that reputation can help to improve the efficiency of blockchain and enhance the fairness of energy trading markets. However, the application of distributed reputation in the energy field has not been fully studied yet. In this paper, we design a distributed reputation system to simulate real-world trust in blockchain-based peer-to-peer energy trading. It is a comprehensive reputation system in the sense that reputation scores are decided by the behavior of participants as consensus nodes, energy buyer, and energy sellers. Its implementation relies on blockchain, especially the smart contract technology, to achieve distributed and automatic reputation management. The distributed reputation system in turn helps to implement a delegated consensus algorithm for blockchain and a reputation-based k -double auction matchmaking scheme for peer-to-peer energy trading. In addition, we define a fairness indicator to capture the reputation-based average benefits and costs when considering reputation as the contribution to the peer-to-peer energy trading market. By simulating the comprehensive system, the numerical results demonstrate the effects of distributed reputation in improving the efficiency of blockchain and balancing fairness indicators between sellers and buyers during peer-to-peer energy trading. As far as we know, this paper is one of the few works to provide a formal method of evaluating the fairness of the peer-to-peer energy trading market. • A distributed reputation system is designed based on the blockchain technology. • Reputation is used to improve blockchain consensus and peer-to-peer energy trading fairness. • A formal definition of fairness of peer-to-peer energy trading is proposed. [ABSTRACT FROM AUTHOR]