SiC MOSFETs are increasingly used in various power electronic converters due to their low switching losses, high operating frequency and high power applicability. The crosstalk phenomenon which will lead shoot-through in bridge-leg configuration and overvoltage breakdown of the device is more serious due to the high switching speed characteristics. In this paper, a smart self-driving crosstalk suppression gate driver is proposed based on the resistor–capacitor–diode (RCD) level shifter circuit for SiC MOSFETs, in which a low impedance branch of Miller clamping circuit is provided for the crosstalk current. In addition, no extra control signal is required which does not increase the complexity of the driver circuit. Then, by modeling the equivalent circuit of the proposed gate driver, the quantization relationship between the clamping capacitor and the crosstalk voltage is derived. Finally, a double-pulse test platform is built to verify the effectiveness of the proposed gate driver under different clamping capacitors, input voltage and load current conditions. The experimental results show that the proposed gate driver can suppress the crosstalk voltage effectively. Meanwhile, the switching loss is reduced by a maximum of 16.6% by using the designed clamping capacitor under 600 V/20 A, while ensuring the switching speed.