This paper presents the fractional-order modeling and steady-state analysis of single-phase quasi-Z-source rectifier (qZSR) with fractional-order inductors and fractional-order capacitors, and aims to explore the influences of the fractional-order inductors and capacitors on the operating characteristics of the single-phase qZSR. The fractional-order circuit model is established based on Oustaloup’s approximation method, the expression of input current, inductor current, capacitor voltage and output voltage are derived and analyzed in detail. Besides, the control strategy and modulation of the FO-qZSR are analyzed. Finally, the simulations are performed based on the circuit model of FO-qZSR in MATLAB/Simulink to verify the theoretical analysis.