This paper investigates a Finite-Control-Set Model Predictive Control (FCS-MPC) for the precise control of (un)balanced load currents in Modular Multilevel Converter (MMC). The control objectives are circulating currents minimization inside the converter arms, achieve a capacitors voltage balance and load current control. To achieve the converter constrained optimization and facilitate the implementation on embedded systems, an integrated perturbation analysis and sequential quadratic programming (IPA-SQP) solver is also utilized. As a case study the proposed approach is applied to a grid-connected five-level MMC. The introduced FCS-MPC formulation reduces sensitivity of the converter output voltage to disturbances in grid side and measurement noise with reducing the computational burden. Simulation results reveal the effectiveness of the developed control scheme in cases when operational objectives, e.g., load current reference tracking and disturbance rejection are considered under system model uncertainties.