In the multi-energy supply microgrid, different types of energy can be scheduled from a “global” view, which can improve the energy utilization efficiency. In addition, hydrogen storage system performs as the long-term storage is considered, which can promote more renewable energy installed in the local consumer side. However, when there are large numbers of grid-connected multi-energy microgrids, the scheduling of these multiple microgrids in real-time is a problem. Because different types of devices, three types of energy, and three types of utility grid networks are considered, which make the dispatching problem difficult. In this paper, a two-stage coordinated algorithm is adopted to operate the microgrids: day-ahead scheduling and real-time dispatching. In order to reduce the time taken to solve the scheduling problem, and improve the scheduling performance, approximate dynamic programming (ADP) is used in real-time operation. Different types of value function approximations (VFA), i.e., linear function, nonlinear function, and neural network are compared to study about the influence of the VFA on the decision results. Offline and online processes are developed to study the impact of the historical data on the regression of VFA. The results show that the neural network based ADP one-step decision algorithm has almost the same performance as the Global optimization algorithm, and the highest performance among all others Local optimization algorithms. The total operation cost relative error is less than 3%, while the running time is only 31% of the Global algorithm. In the neural network based ADP, the key technology is continuously updating the training dataset online, and adopting an appropriate neural network structure, which can at last improve the scheduling performance.