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This paper presents a new finite control set model predictive control strategy that, contrary to conventional approaches, achieves (i) zero steady-state error in the converter's AC current, and (ii) both fixed and lower harmonic spectrum, similar to that achieved by pulse width modulation based control schemes. These characteristics are attractive for medium and high voltage applications where high dv/dt is prohibitive and reduced switching losses are a must, or in applications that use passive filters and where a spread harmonic spectrum can cause resonances. The proposed strategy achieves dynamic results similar to those of conventional predictive control and a steady-state performance similar to that of a modulated control strategy. To do so, the strategy utilizes a modulated integral action to incorporate an input restriction into a conventional predictive control cost function. A grid-connected cascaded H-Bridge multilevel inverter is used to validate the strategy. Simulated and experimental results in both steady and transient states are presented to verify the proposed strategy's performance in the converter.