With the increasing penetration of distributed energy resources into islanded microgrids, a grid-forming inverter (GFI) has become the key element interfacing renewable energy sources. Usually, the GFI is employed with an output filter to minimize the harmonic content achieving high-quality output voltage regulation. To this end, model-predictive control (MPC) has been widely proposed to control the output voltage of GFI systems due to the high-quality performance, fast control response, and straightforward handling of constraints. However, an accurate model of the system is required for the conventional MPC to avoid a suboptimal performance under uncertainties. To overcome this known drawback, a novel model-free predictive control is proposed in this article. Consequently, the output voltage of an LC L-filtered GFI is regulated without the knowledge of the physical model.