This paper focuses on the design of a snubber circuit for Solid State Circuit Breaker (SSCB) based on SiC MOSFET. It analyzes the operation principle and pros and cons of existing snubber circuit. Based on the analysis, a novel bidirectional snubber circuit suppressing fault current quickly and simultaneously protecting overvoltage on SiC MOSFET is proposed. The operation principle of the proposed snubber circuit is discussed, and design criteria for the snubber circuit are addressed for the case that the source inductance and the load inductance of SSCB are asymmetrical. Through the computer simulation results, it is shown that the proposed snubber circuit is effective in suppressing fault current and keeping the voltage across SiC MOSFETs under tolerable range. A prototype bidirectional SSCB with the proposed snubber circuit is constructed and tested against the short circuit fault at load side and source side. The test results confirm the effectiveness of the proposed snubber circuit for the suppression of fault current and protection from the overvoltage on the SiC MOSFET.