The line impedance between the DG units are always different in the islanded AC microgrid, which can result in circulating current and unreasonably sharing reactive power among inverters by using conventional droop control method. To solve this problem, an improved droop control strategy of adaptive virtual impedance based on fuzzy controller is proposed. The central controller calculates the reactive power difference between them and the variation of the reactive power difference. And then it sends the calculated results to each inverter. The fuzzy controller adaptively adjusts the virtual impedance by using the reactive power information of the inverter to compensate for the voltage drop difference caused by the inconsistent equivalent impedance, thereby achieving reactive power sharing. At the same time, in order to solve the problem of the voltage drop of inverter output voltage, a voltage compensation unit is introduced to restore the output voltage to the rated value. Finally, simulations are performed in MATLAB/Simulink to verify the validity of the proposed control strategy.