Based on fractional calculus and the fact that the capacitor and the inductor are fractional in nature, the fractional mathematical model and the fractional state averaged model of the Boost converter in continuous conduction mode operation are built and analyzed. Also, the condition for the continuous conduction mode operation of the Boost converter is given. Finally, in order to verify the theoretical analysis, the simulation model of the Boost converter in continuous conduction mode operation is established by using the software of Matlab/Simulink.