High switching-speed Silicon Carbide Metal-Oxide-Semiconductor Field-Effect Transistor (SiC MOSFET) has serious crosstalk issues. During the turn-ON transition and turn-OFF transition of the active switch in a phase-leg configuration, the voltage drops across the common-source inductor and the displacement current of the gate-drain capacitor of the OFF-state switch induce a spurious pulse on its gate-source voltage. This paper proposes a new gate driver using two Bipolar Junction Transistors (BJTs) and one diode to connect the gate terminal of SiC MOSFET and the negative driver voltage, which provides a low impedance path to bypass the displacement current of the gate-drain capacitor when crosstalk issues occur. The simulation results prove the proposed driver is valid on suppressing the crosstalk issue. The comparisons between the prior drivers and the proposed driver show the superiority of the proposed driver. Finally, the proposed gate driver is successfully implemented and experimentally verified on a 1.1 kW synchronous buck prototype.