As for the problem of unbalanced current output from the inverter due to the unbalanced load in the island microgrid, a current compensation strategy based on Fourth Order Generalized Integrator (FOGI) for fundamental wave positive sequence current separation is proposed. The method uses the FOGI to construct the unbalanced current compensation strategy based on fundamental wave positive sequence component separation, which compensates the unbalanced current in the microgrid. The compensation results comparison of FOGI and Second-Order Generalized Integrator (SOGI) shows that FOGI has stronger compensation ability than SOGI, and can compensate the unbalanced current on the line fully. Simulation results show that the proposed method has better imbalance compensation ability and harmonic suppression ability. This work is supported by National Natural Science Foundation of China (No.61275038).