Recent advancement of distributed renewable generation has motivated microgrids to trade energy directly with one another, as well as with the utility, in order to minimize their operational costs. Energy trading among microgrids, however, confronts challenges such as reaching a fair trading price, maximizing participants’ profit, and satisfying power network constraints. In this paper, we formulate the direct energy trading among multiple microgrids as a generalized Nash bargaining (GNB) problem that involves the distribution network's operational constraints (e.g., power balance equations and voltage limits). We prove that solving the GNB problem maximizes the social welfare and also fairly distributes the revenue among the microgrids based on their market power. To address the nonconvexity of the GNB problem, we propose a two-phase approach. The first phase involves solving the optimal power flow problem in a distributed fashion using the alternative direction method of multipliers to determine the amount of energy trading. The second phase determines the market clearing price and mutual payments of the microgrids. Simulation results on an IEEE 33-bus system with four microgrids show that the proposed framework substantially reduces total network cost by 37.2%. Our results suggest direct trading need be enforced by regulators to maximize the social welfare.