The implementation of traditional finite-control-set model predictive control (FCS-MPC) with variable switching frequency in voltage source rectifiers (VSRs) can make the system suffer from poor current harmonics performance. In fact, the resulting wide-spread voltage harmonic generated at the AC terminals makes the design of the typical multi-order AC filtering bulky and prone to control instabilities. This paper proposed a fixed frequency carrier-based modulated model predictive control (CB-MMPC) which is able to overcome these issues. This control strategy aims to improve the total harmonic distortion (THD) of the AC current waveform without introducing any additional weight factor in the cost function of the optimization routine, while maintaining the typical performance of fast current dynamic response of the FCS-MPC. Herein, the detailed implementation of the proposed CB-MMPC is given, while considering its application to the current feedback control loop of a three-phase three-level Vienna rectifier. Finally, PLECS based simulation results are used to verify the feasibility and the effectiveness of the proposed control strategy and to benchmark its performance to the classical FCS-MPC strategy and the conventional application of a current closed loop implementing a proportional-integral(PI)-controller.