This paper proposes a sequential Phase-Shifted Model Predictive Control (PS-MPC) strategy for multicell power converters. The key novelty of this proposal lies in the way the predictive control strategy is formulated to fully exploit a phase-shifted pulse width modulation (PS-PWM) stage. Normally, when using a linear controller along with a standard PS-PWM stage, the modulator receives the same duty cycle for all the internal carriers. In contrast, by means of an appropriate choice of synchronized models for each carrier, the proposed predictive controller obtains independent optimal duty cycles for each carrier in a sequential manner. This allows one to formulate the optimal control problem to govern not only the output current but also the internal floating capacitor voltages, similarly to the finite-control-set MPC (FCS-MPC) case. As a result, the proposed sequential PS-MPC can attain a faster floating voltage balancing dynamic when compared to a standard PS-PWM implementation. Moreover, it generates a fixed-spectrum in the steady state with a constant commutation rate, which outperforms a standard FCS-MPC strategy. Simulation results of the proposed sequential PS-MPC strategy governing a single-phase four-level flying capacitor converter are presented to verify its dynamic and steady-state performance.