This paper is given a full detail of mathematical analyses of input current and output voltage for a novel active type power factor correction (PFC) converter. These are compared with harmonics components of input current for a conventional PFC converter. The proposed PFC converter is constructed in using a new loss-less snubber circuit to achieve a soft switching of control device. Also the proposed converter for discontinuous conduction mode (DCM) eliminates the complicated circuit control requirement and reduces the size of components. The input current waveform in the proposed converter is got to be a sinusoidal form of discontinuous pulse in proportion to magnitude of ac input voltage under the constant duty cycle switching. Therefore, input power factor is nearly unity and the control method is simple. Particularly, the stored energy of loss-less snubber capacitor is recovered with input side and increases input current from resonant operation. The result is that input power factor of the proposed converter is higher than that of conventional PFC converter. Some simulative results on computer and experimental results are included to confirm the validity of the analytical results.