In this paper, a new ZCT-ZVT PWM interleaved DC-DC boost converter with an active snubber cell is proposed. By considering interleaved approach, this topology minimizes the ripple of the output voltage and input current. Also, it provides to be reduced the extra current stress on the main devices. In proposed new converter, all of the semiconductor components softly turn on and turn off with Zero Voltage Switching (ZVS) or Zero Current Switching (ZCS). The main feature of proposed converter is that the extra current and voltage stresses do not occur on the main switches and main diodes. Also, the current stress on the auxiliary switch is at acceptable level. In the proposed converter, the main switch perfectly turns on with Zero Voltage Transition (ZVT) and turns off with Zero Current Transition (ZCT). Therewith, the auxiliary switch turns on with ZCS and turns off with ZVS. Additionally, the proposed converter smoothly operates under light load conditions and wide input line voltage. Another advantage of this converter is that the soft switching is achieved by just one auxiliary switch. The theoretical analysis of the proposed converter is made. The operating stages, the waveforms and the simulation results of the proposed converter operated for 1.5 kW and 100 kHz is given in detail.