Due to lack of kinetic energy, the power electronic inverters based renewable energy microgrids have no inherent inertia capability to address the power swings. This degrades the transient response in island or weak-grid connected operational modes during disturbances. To address this issue, an important evolution that has been cited in the literature is, design of droop control techniques with the capability of virtual inertia injection to strengthen the frequency response during transients. But, adaptivity and voltage response aspects have not been covered. So, to address these issues, this paper proposes modified droop control technique using fuzzy logic based injection of adaptive virtual moment of inertia. The philosophy involved in the design is, varying the p-w and q-v droop coefficients adaptively with respect to frequency and voltage deviations occurred during disturbances. So, the droop controller can efficiently cope-up with disturbances and provide better frequency/voltage response during transients. The efficacy of the proposed technique is analyzed using MATLAB/Simulink®. From results, it is seen that the proposed technique improved voltage and frequency transient response over the conventional technique by providing adaptive control action during disturbances in microgrids. © 2017 IEEE.