Based on the autonomous character of one-cycle control, the average model of one-cycle controlled Cuk power factor correction converter can be derived. Subsequently, the approximate analytical expressions of periodic solutions are obtained by using the harmonic balance method. Furthermore, through analyzing the changing trend of Floquet multipliers, the location and the type of the first bifurcation point are predicted. Thus, the intrinsic mechanism of such an instability can also be explained. The results show that the intermediate-scale instability is due to the loss of stability of periodic solutions, which is named the Neimark-Sacker bifurcation in the circuit system. Finally, experimental results are presented for verification purpose. Our work has revealed the salient feature of the intermediate-scale instability, and provided a theoretical basis for facilitating design of the converter.