Classic synchronization closing detection method of microgrid needs the tedious process to simultaneously compare the voltage phase, amplitude and frequency on both sides. Synchronization closing detection method of microgrid based on mutual approximate entropy is proposed, which only needs the single value of mutual approximate entropy to compare the voltage similarity on both sides. The principle and advantage of synchronization detection closing method of microgrid based on mutual approximate entropy are analyzed. And the key issue such as the value setting of the method is studied. Then the implementation steps of the method is introduced in detail. Finally the simplified model of microgrid connecting to distribution network is constructed in Matlab, where the value of mutual approximate entropy is simulated on the change of voltage phase, amplitude and frequency. The simulation result verifies the effectiveness of the method.