Local electricity markets are emerging solutions to enable local energy trade for the end users and provide grid support services when required. Various models of local electricity markets (LEMs) have been proposed in the literature. The peer-to-peer market model appears as a promising structure among the proposed models. The peer-to-peer market structure enables electricity transactions between the players in a local energy system at a lower cost. It promotes the production from the small low–carbon generation technologies. Energy communities can be the ideal place to implement local electricity markets as they are designed to allow for larger growth of renewable energy and electric vehicles, while benefiting from local transactions. In this context, a LEM model is proposed considering an energy community with high penetration of electric vehicles in which prosumer-to-vehicle (P2V) transactions are possible. Each member of the energy community can buy electricity from the retailer or other members and sell electricity. The problem is modeled as a mixed-integer linear programing (MILP) formulation and solved within a decentralized and iterative process. The decentralized implementation provides acceptable solutions with a reasonable execution time, while the centralized implementation usually gives an optimal solution at the expense of reduced scalability. Preliminary results indicate that there are advantages for EVs as participants of the LEM, and the proposed implementation ensures an optimal solution in an acceptable execution time. Moreover, P2V transactions benefit the local distribution grid and the energy community.