Based on the fact that the inductor and the capacitor are fractional in nature, the fractional order mathematical model of the Boost converter in pseudo-continuous conduction mode is established by using fractional order calculus theory. According to the state average modeling method, the fractional order state average model of Boost converter in pseudo-continuous conduction mode is built. In view of the mathematical model, the inductor current and the output voltage are analyzed and the transfer functions are derived. Then the differences between the integer order and the fractional order mathematical models are analyzed. On the basis of the improved Oustaloup fractional order calculus for filter approximation algorithm and the model of fractional order inductance and capacitance, the simulation results have been compared between the mathematical model and circuit model with Matlab/Simulink software; the origins of model error are analyzed and the correctness of the modeling in fractional order and the theoretical analysis is verified. Finally, the differences and the relations of Boost converter among the continuous conduction mode, the discontinuous conduction mode, and the pseudo-continuous conduction mode are indicated.