Grid-forming inverters (GFI) play an important role as power interfaces for distributed generation units in islanded microgrids, where inductive-capacitive-inductive (LCL) output filters are commonly employed to mitigate the harmonics injected by voltage-source inverters. Due to advantages such as fast dynamic response and straightforward handling of constraints, Finite-control-set model predictive control (FCS-MPC) has become an attractive option for voltage control in GFI systems. However, conventional FCS-MPC algorithms with short prediction horizon have performance limitations in the tracking of ac references in systems with high-order dynamics, such as LCL-filtered GFIs. On the other hand, predictive algorithms with extended prediction horizons suffer from an increased computational burden. This paper proposes a new FCS-MPC algorithm to accurately control the capacitor voltage in an LCL-filtered GFI, using a discrete-time prediction model to dynamically compute the reference for a FCS-MPC inverter-side current controller. The main advantages of the proposed method are its simple implementation without requiring the tuning of weighting factors in its cost function; and its short prediction horizon, which maintains a reduced computational cost. Moreover, active resonance damping elements such as digital filters or ad hoc feedback loops to deal with the LCL filter resonance are not required. Simulation tests and experimental results in a laboratory-scale setup confirm the effectiveness of the proposed control algorithm, yielding lower distortion of output voltage waveforms and increased robustness to modeling errors compared with the conventional FCS-MPC approach.