An internal model control with conditional integrator is proposed for the robust output regulation of single-switch quadratic buck converters. The output regulation problem of a quadratic buck converter is converted to the stabilization of an augmented system consisting of the buck converter and the internal model. The design procedures include the design of an internal model with conditional integrator and a robust state feedback stabilizer with saturation behavior. The closed-loop stability of the converter will be theoretically analyzed. Finally, the effectiveness of the proposed control scheme for large load and supply variations are also tested. The design of the controller does not require the exact circuit parameters and the stability proof demonstrates the robustness against parameter uncertainties.