This paper presents a model predictive control for the quantum series-parallel LCC-type resonant converter. A hybrid model for the converter including the autonomous change of the systems structure by the output rectifier of the converter is derived. By solving the piecewise linear state equations for the possible input voltages, generated by an II-bridge, the change of the output voltage can be calculated. The maximum resonant current and the voltage across the series-resonant capacitor at the next zero crossing of the resonant current can be estimated, too. Simulation results and measurements show the effectiveness of the control algorithm with constrained resonant current and multistep prediction.