Owing to its characteristics of high voltage gain and low voltage stress, the modified SEPIC converter is widely applied in fields such as photovoltaic and uninterruptible power supply. At the same time, because of its satisfying soft switching characteristic, it can also be applied to high-frequency scenarios to improve the power density. To expand the load range and improve the dynamic response, the establishment of a mathematical model is important. In this paper, the generalized state-space averaging method is adopted to model a quasi-resonant modified SEPIC converter based on switched inductor, the corresponding small signal model is established, and the transfer function of system output is obtained. The K-factor method is used to design a compensator, thus optimizing the system's dynamic performance. A digital control method of constant-current output was designed, which was further verified by experimental results.