The multi-modular converter (MMC) technology is becoming the preferred option for the increased deployment of variable renewable energy sources (RES) into electrical power systems. MMC is known for its reliability and modularity. The fast adjustment of the MMC’s active/reactive powers, within a few milliseconds, constitutes a major research challenge. The solution to this challenge will allow accelerated integration of RES, without creating undesirable stability issues in the future power system. This paper presents a variant of model predictive control (MPC) for the grid-connected MMC. MPC is defined using a Laguerre function to reduce the computational burden. This is achieved by reducing the number of parameters of the MMC cost function. The feasibility and effectiveness of the proposed MPC is verified in the real-time digital simulations. Additionally, in this paper, a comparison between an accurate mathematical and real-time simulation (RSCAD) model of an MMC is given. The comparison is done on the level of small-signal disturbance and a Mean Absolute Error (MAE). In the MMC, active and reactive power controls, AC voltage control, output current control, and circulating current controls are implemented, both using PI and MPC controllers. The MPC’s performance is tested by the small and large disturbance in active and reactive powers, both in an offline and online simulation. In addition, a sensitivity study is performed for different variables of MPC in the offline simulation. Results obtained in the simulations show good correspondence between mathematical and real-time analytical models during the transient and steady-state conditions with low MAE. The results also indicate the superiority of the proposed MPC with the stable and fast active/reactive power support in real-time simulation.