In order to tackle the challenge of centralized reinforcement learning based microgrid energy management would impose severe privacy violation and consume a large number of communication resource, we address the problem of microgrid energy management strategy (EMS) based on edge-cloud assisted federated deep reinforcement learning (FDRL). We first present the microgrid operation model in edge-cloud computing scenario to optimize energy management strategy with economic benefits as the goal. Then, the federated dueling deep Q-network with novel action exploration (DDQN) is proposed to resolve the problem model and it is leveraging to design an innovative microgrid energy management strategy, and the convergence and computational complexity of the proposed energy management strategy is analyzed. Simulation results validate that the reward and profit obtained with the edge-cloud-assisted federated DDQN energy management strategy outperform the conventional deep reinforcement learning (DRL) method, and the communication efficiency and data privacy preservation can be attained.