In this paper, a distributed peer-to-peer (P2P) electricity trading model was proposed to study economic interactions between load aggregators (LAs) and microgrid operators (MGOs) considering network losses in a distribution system. In this model, the economic interactions among market participants were formulated as a Nash bargaining game, where LAs and MGOs can bargain with each other on the trading volume of electricity and payment. To achieve the Nash bargaining solution, the game was divided into two sub-problems: social welfare maximization and payment bargaining. Then, the alternating direction method of multipliers was used to solve the two sub-problems with limited information exchange. Finally, we tested the proposed model on a 12 × 12 km2 distribution system, and the results verify its effectiveness.