The proposed converter includes: three boost inductors, three filter capacitors, six main switch modules each having a switch element, a diode and a resonant capacitor, two auxiliary switches, two main diodes, a resonant inductor, and two output capacitors. A control circuit is employed for generating driving signals from six SPWM signals to drive the six main switches and the two auxiliary switches of the converter. A six-step control method is employed to adjust the SPWM signals and a soft-switching method is employed to generate the driving signals to turn on/off the six main switch modules and the two auxiliary switches when the voltage on the second terminal of each main switch module/auxiliary switch is zero and the current flows into each auxiliary switch is zero to correct the power factor.