This paper proposes an inductor current sensorless control strategy based on modified virtual synchronous generator (VSG) method for single-phase inverter-interfaced microgrid application. Firstly, the outer power loop with Q-U integral term is presented for output reactive power enhancement, and an inner voltage regulation loop based on luenberger state observer is proposed to reduce the inductor current sensor. Meanwhile, in order to improve the response speed of the observer, the luenberger observer is designed based on the optimal pole assignment method. Secondly, a seamless switching strategy based on the modified VSG method is proposed, which can realize the seamless transition between the island mode and grid-connected mode. Finally, a single-phase 3kW VSG prototype is built, and the effectiveness and correctness of the proposed control strategy is verified by the simulation and experimental results.