In this paper a new nonlinear identification method for microgrids based on neural networks is proposed. The system identification process can be done using the available closed-loop system input/output data recorded during normal operation without additional external excitation, while disturbances between different distributed energy resources are considered to improve the identification accuracy. Moreover, Based on the nonlinear identified model, a novel distributed frequency/voltage regulation and active/reactive power sharing control framework is developed. The new control strategy does not rely on the classical droop -based hierarchical control structure, such that improved transient performance and accurate power sharing for microgrid with mixed lines can be achieved. Furthermore, the anti-windup technique is incorporated into the controller design process to guarantee that the input constraints are satisfied and the voltage deviations are within an acceptable range. The effectiveness of the proposed method is demonstrated via simulations.