The absence of rotational masses from synchronous generators in converter-interfaced microgrids leads to a lack of inertia. Consequently, the system exhibits steeper frequency variations and higher frequency nadir, which may degrade the dynamic performance and challenge the operation of sensitive equipment such as protective relays in the grid. Virtual synchronous generator is introduced as an effective solution to increase the inertial response of converter interfaced renewable energy sources. This article proposed a fuzzy controller, which is augmented on the virtual synchronous generator topology to damp the perturbation during transients by increasing the inertia of the system. The proposed fuzzy control adds a correction term to the governor's output power that increases the system inertia during transients. In order to compare the inertial response improvement, a comparison between proposed fuzzy control technique and cost function based inertia and damping coefficient optimization is done on a virtual synchronous generator platform. It is shown that online measurement based adaptive methods have a better inertial response against other time-consuming techniques. To further verification, a number of experiments are done, which confirm the merits of the proposed fuzzy based virtual synchronous generator control method.