A quadratic buck converter, whose voltage conversion ratio equals square of a duty cycle, has good potential in DC-DC converter applications where a large voltage step-down is required, such as in modern automobile. This paper presents dynamic modeling of a quadratic buck converter with the State-Space averaging (SSA) technique. The SSA modeling leads to a small-signal linear dynamic model of the converter, from which the transfer functions used for feedback control design can be determined. Results are presented to verify accuracy of the obtained model.