Abstract: In order to study the optimal clearing problem of consumers in a fully decentralized peer-to-peer（P2P） energy market, this paper focused on solving the challenges of cooperation among consumers and maximizing social welfare in P2P markets. A new parallel and distributed alternating direction method of multipliers（ADMM） is adopted to derive the trading mechanism of P2P market. This method considers the utility function of each prosumer, and introduces a distributed generator（DG） and a battery energy storage system（BESS）. In the algorithm, each prosumer synchronously exchanges a small amount of information with its neighboring prosumers through iteration and optimizes to meet different requirements. The effectiveness of the proposed method is demonstrated by numerical verification of the 6-peers system. Compared with the pool-based trading mechanism, the fully decentralized P2P problem increases the transaction power by 160% per unit time, and the social welfare increases from-9.47 yuan to 32.43 yuan.