Data centers are facing a major challenge improving the energy consumption efficency, particularly given the increasing demand for data in the last years. To this end, power supplies became a crucial factor dealing with this issue. To increase the efficiency, high step-down topologies with fewer switches are an attractive solution for telecom systems. The quadratic buck converter (QBC) is a suitable choice for this purpose. However, due to its nonlinear behavior, the converter's control stability is one of the main challenge. In such cases, finite control set model predictive control (FCS-MPC) solves the control challenge in nonlinear systems. However, despite the fast and stable performance of the predictive control, the need for the load information and the sensitivity to avoid parameter mismatch is not completely solved using classical FCS-MPC. Therefore, this work proposes a model-free predictive control (MF-PC) method to the quadratic buck converter increase the robustness under parameter mismatch preserving the advantages of model predictive control, such as fast dynamic response and low current ripple.