This study proposes an advanced control scheme for the interlinking inverters of the hybrid AC/DC microgrids, which facilitates a seamless transition between grid-connected and stand-alone/islanding modes for the microgrid. Due to a nonlinear relationship between the terminal voltages of the voltage-source inverter (VSI) interfacing through inductor–capacitor (LC) filters with the grid voltages and currents, a feedback linearization technique (FLT) is employed to control the interlinking VSI under both grid-connected and islanding operations. The FLT-based current controllers are applied in the grid-connected mode, in which they adjust the power exchange between the DC and AC subgrids and mitigate the distortion of the grid currents produced by nonlinear loads. Under the stand-alone operation, the AC bus voltages are directly regulated by the FLT-voltage controllers of the interlinking VSI. In order to reduce the inrush currents and voltage overshot at the instant of mode switching, the FLT-based controllers are performed all the time regardless of the operating modes, where the voltage references for the VSI are not changed abruptly. The control performance of the VSI is highly satisfactory with low-transient overshoot values of the voltages and currents and low total harmonic distortion (THD) values of the grid currents and AC bus voltages are about 3.5% and 2.7%, respectively, under the nonlinear load condition. The validity of the new control strategy is verified by the simulation work, which investigates the operation of a hybrid AC/DC microgrid.