Based on the generalized gradient approximation, we have investigated the phase transition of 3C-SiC from ZB to NaCl structure using first-principles method, and obtained the accurate symmetry Imm2 (previously regarded as lower symmetry Cmm2 and Pmm2) of the intermediate phase. The relative activation enthalpy 0.647eV is close to the result of Catti. The obtained transition pressure 69GPa is lower than the experimental value of 100GPa which may be attributed to the hysteresis of the phase transition. Meanwhile, the energy bands for ZB- and NaCl-SiC were also calculated and discussed, the results suggest that the phase transition of 3C-SiC is accompanied by an electronic transition from semiconducting to metallic character besides the structure reconstruction, which may be useful for the accurate determination of the transition pressure.