This paper presents a study on using the interleaved quadratic buck converter (QBC) to power an electrolyzer system for green hydrogen production. The interleaved operation of QBC offers several advantages, including high current output, reduced current ripple, lower input and output voltage stresses, and improved reliability, making it an excellent choice for high-power applications. The finite control set model predictive control (FCS-MPC) is proposed to control the QBC and regulate the system variable. FCS-MPC enables the control of the phase-shift required for interleaved operation, which is achieved through an extra term added to the cost function. Simulation results confirm the precise regulation of the output voltage and the reduction in output current ripple while effectively handling system disturbances.