This paper presents the model-based predictive current control (MPC) applied to a four-wire three-phase STATCOM based on the three-level H-Bridge converter. The main advantages of MPC are its simplicity, easy inclusion of restrictions and fast dynamic response. However, MPC uses a variable switching frequency and this causes a lot of current ripple and a high total harmonic distortion (THD). This article proposes a modulation strategy, at a fixed switching frequency, in order to mitigate the propagation of the THD of the current injected in the point of common coupling (PCC). It is considered a critical operation of the STATCOM operating with a fault on one of the phases of the electrical network. Theoretical results based on simulations are provided to show the performance of the proposed control.