Conventionally, the dual-loop PI controllers are designed for the single-phase boost power factor correction (PFC) converters operating under continuous conduction mode (CCM), which is not available to perform rapid adaptations to plant uncertainties caused by the different operation modes and the parameter variations. In order to improve the control performance and robustness, a cascaded model-free predictive control (MFPC) scheme is proposed based on the unified ultra-local model under CCM and discontinuous conduction mode (DCM) for the single-phase boost power factor correctors. Different from the traditional sluggish PI controllers, the proposed control law is adaptive to the operation mode and sudden variations with the algebraic identification technique, thus providing high-quality line current and fast dynamic characteristic for the full power operating range. Comparative simulations and experiments with PI control scheme are provided to certificate the effectiveness of the proposed control scheme.