In this paper, a Boost converter model in the pseudo-continuous conduction mode(PCCM) of inductive current based on the definition of R-L fractional-order is studied. On this basis, the state-space averaging model of the converter is derived. Then, the expressions for the step-up ratio, DC static operating point, inductive current ripple, and output voltage ripple are derived. Results show that compared with the corresponding expressions derived on the basis of the definition of Caputo fractional-order, the derived expressions for DC static operating point and step-up ratio under the definition of R-L fractional-order are related to both the duty cycle and the orders of the capacitor and inductor. The expression for output voltage ripple is not only related to the order a of fractional-order inductor, but also related to the order ? of fractional-order capacitor. Therefore, the orders of inductor and capacitor obviously affect the DC component of state variables and the stable-state characteristics of factional-order PCCM Boost converter. Finally, a mathematical model and a circuit model of the R-L fractional-order PCCM Boost converter are built in MATLAB/SIMULINK, and simulation results show that the analysis result of the R-L fractional-order PCCM Boost converter model is more stable than that of the other PCCM Boost model, and the corresponding error is smaller.