In this study, a model predictive control (MPC) strategy that combines finite-control-set MPC with selective harmonic elimination (SHE) modulation pattern in its formulation is proposed to govern multilevel power converters. Based on a desired operating point for the system state (converter current reference), an associated predefined SHE voltage pattern is obtained as a required steady-state control input reference. Then, the cost function is formulated with the inclusion of both system state and control input references. According with the proposed reference and cost function formulation, the predictive controller prefers to track the converter output current reference in transients, while preserving the SHE voltage pattern in steady state. Hence, as evidenced by experimental results, a fast dynamic response is obtained throughout transients while a predefined voltage and current spectrum with low switching frequency is achieved in steady state.