This paper presents the modeling of a Quadratic Buck Converter with interleaved function, operating in continuous conduction mode. The structure of the proposed converter presents better functional aspects with respect to other Quadratic Buck converters reported in the literature. This work establishes the general structure of the proposed converter, as well as its operation. In addition, the switching model and the average model are developed in order to obtain the dynamic characteristics of the system, which are used for the design of the controllers.