Microgrid (MG) cooperation, which allows information and energy exchange among multiple MGs, can improve the reliability of MGs and thus becomes a promising technique for multi-microgrid (MMG) systems. Since MG is generally selfish in nature, how to motivate MGs to participate in MG cooperation becomes an important issue. To do this, a Stackelberg game theoretic framework to MG cooperation, called the MG energy trading game (MGETG), is proposed. In the MGETG, an MMG center as the leader motivates and regulates the MG cooperation by setting the energy trading prices. Then, MGs as the followers determine their energy trading strategies so as to maximize their utilities. Nikaido-Isoda relaxation algorithm is applied to find the Nash equilibrium of MGs actions and a pricing algorithm is devised to find the energy trading price based on the golden section search. Our simulation results show that the proposed algorithms can improve the renewable utilization by 25.9% and reduce the total operation cost by 35.5% through MG energy trading.