Buck-Buck/Boost power factor correction (PFC) converter is a great choice to compensate the inherent dead zones in the input current of Buck PFC converter. However, whether the converter operates with traditional constant on-time control (COTC) in critical conduction mode (CRM) or with conventional constant duty-cycle control (CDCC) in discontinuous conduction mode (DCM), the power factor (PF) is low, especially at low input voltage. Therefore, fixed on-time ratio control (FOTRC) and fixed duty-cycle ratio control (FDCRC) are proposed for CRM/DCM Buck-Buck/Boost PFC converter to achieve high PF, respectively. Both control methods maximize PF over wide input voltage range by adjusting on-time or duty-cycle of Buck/Boost mode and Buck mode. Compared with the traditional controls, the proposed control methods also have advantage of increasing efficiency. Furthermore, for improving dynamic response performance, smooth and rapid dynamic response control (SRDRC) is put forward, which can reduce the regulation time and output voltage overshoot/undershoot when the load or input voltage changes abruptly. In addition, the implementation circuits combining FOTRC/FDCRC and SRDRC are designed. Two prototypes have been built and tested in the lab to demonstrate the validity of the theoretical analysis.