A grid-forming inverter (GFI) is an important component for the operation of an islanded microgrid. Its purpose, similar to a conventional slack bus generator, is to build up a reference voltage for other distributed generating units in the microgrid. Usually, a nested-loop proportional plus integral (PI) control structure is employed to control a GFI in a dq reference frame. However, conventional PI-based nested-loop control method has a deteriorative performance under parameter variations. In this paper, a novel nested-loop control strategy is proposed for control of a GFI system containing an LC output filter and loads. The proposed method does not require a precise model for the inverter system and can better deal with uncertainties and LC filter resonance without using any passive or active damping mechanisms. It utilizes a sliding-mode control in the inner current loop and a mixed H₂/H_∞ optimal control in the outer voltage loop, which provides the advantages of constant switching frequency, low total harmonic distortion, robustness against parameters variations, and fast transient response. The simulation and hardware experiments presented in this paper demonstrate the proposed controller's improved transient and steadystate performance in various key criteria, over conventional PI-based nested-loop control strategy.