This paper proposes a wide-range multi-sample peak digital predictive current mode control (DPCMC) for a 3-level flying capacitor buck (3-LFCB) converter. The main advantage of this controller is its ability to cover the entire duty-cycle range without encountering flying capacitor (FC) instability issues. The proposed control strategy maintains the FC voltage well-balanced without the need for measurement or estimation. Additionally, the control performs effectively at the operating point where the output voltage is half the input voltage, a condition generally avoided by most existing control strategies. The algorithm's performance is demonstrated through both simulation and experimental results on a 3-LFCB prototype.