The stability of a Cuk power factor correction(PFC) converter in discontinuous inductive current mode is analyzed in detail when the system load changes. Based on the working characteristics of the PFC converter and according to the harmonic balance method and Floquet theoretical analysis, results show that when the load resistance becomes smaller(i.e., the light load is changed to heavy load), a period-doubling bifurcation of power frequency will occur in the sys-tem. The resistance value is given when the system undergoes the period-doubling bifurcation. At the same time, the system's unstable and stable boundary regions which are composed of load resistance, output inductance and input voltage are also given when the output inductance and input voltage change. In addition, based on the phase orbit diagram of input inductor current-output voltage and the harmonic analysis spectrum of output voltage, the dynamic behavior of the system can be better observed. Finally, the theoretical analysis was verified by experimental results.