This paper presents a robust H∞ control technique for an islanded microgrid in the presence of sudden changes in load conditions. The proposed microgrid scheme consists of a parallel connected inverter with distributed generations. When the load is suddenly changed the frequency deviates from its nominal value. The objective is to design a robust frequency droop controller in order to achieve the frequency at nominal values without using any secondary controller and communication systems while improving power sharing accuracy. Small signal modeling of the power system is designed for the formulation of the problem and the H∞ optimal linear matrix inequality technique is applied in order to achieve the objectives. The proposed controller has been tested with the MATLAB/ SimPowerSytem toolbox.