In power converters, common challenge for current reference tracking employing model predictive control (MPC) is the high computational burden. This issue is more obvious when solving optimal control problems over prediction horizons. To manage and enhance the computational efficiency of widely used control strategies, an integrated perturbation analysis and sequential quadratic programming (IPA-SQP) solver is used to achieve the system constrained optimization and lower sampling times, hence reducing the computational complexity. A Finite-Control-Set Model Predictive Control (FCS-MPC) for current control in cascaded H-bridge Modular Multilevel Matrix Converter (M3C) is also developed. The M3C is connected to a low frequency AC system, which has an operating frequency less than 20 Hz. The proposed control scheme is therefore introducing an alternative for practical implementation. Simulation results for a closed-loop system with low frequency output side for a 9-level M3C is included to validate the main findings.