<p>Peer-to-peer (P2P) energy trading is one of the promising approaches for implementing decentralized electricity market paradigms. In the P2P trading, each actor negotiates directly with a set of trading partners. Since the physical network or grid is used for energy transfer, power losses are inevitable, and grid-related costs always occur during the P2P trading. A proper market clearing mechanism is required for the P2P energy trading between different producers and consumers. This paper proposes a decentralized market clearing mechanism for the P2P energy trading considering the privacy of the agents, power losses as well as the utilization fees for using the third party owned network. Grid-related costs in the P2P energy trading are considered by calculating the network utilization fees using an electrical distance approach. The simulation results are presented to verify the effectiveness of the proposed decentralized approach for market clearing in P2P energy trading.</p>