In practice, most systems have fractional-order characteristics. Therefore, the modeling based on fractional-order calculus theory can describe the system behavior more accurately, and fractional-order PID controllers instead of integer-order PID controllers can achieve better system performance. In this paper, the Oustaloup algorithm is used to perform the fifth-order fitting of s^0.8 at first. Then, the fifth-order fitting fractional-order inductance and capacitance model is constructed, which is simplified compared with the tenth-order model. Based on the establishment of the fractional-order mathematical model of a Boost converter, a full fractional-order system of the Boost converter with voltage-current double closed-loop is formed by using the fractional-order PID controller. The fractional-order circuit model, fractional-order mathematical model, and full fractional-order system are simulated using software MATLAB, and results show that the fractional-order model can describe the characteristics of the Boost converter more accurately, while the full fractional-order system controlled by the fractional-order PID has satisfying steady-state and dynamic performances.