Bifurcation behaviours of the peak current controlled power-factor-correction (PFC) boost converter, including fast-scale instability and low-frequency bifurcation, are investigated in this paper. Conventionally, the PFC converter is analysed in continuous conduction mode (CCM). This prevents us from recognizing the overall dynamics of the converter. It has been pointed out that the discontinuous conduction mode (DCM) can occur in the PFC boost converter, especially in the light load condition. Therefore, the DCM model is employed to analyse the PFC converter to cover the possible DCM operation. By this way, the low-frequency bifurcation diagram is derived, which makes the route from period-double bifurcation to chaos clear. The bifurcation diagrams versus the load resistance and the output capacitance also indicate the stable operation boundary of the converter, which is useful for converter design.