Based on density function theory with the ultrasoft pseudopotential scheme in the frame of the generalized gradient approximation, the structural, mechanical, and electronic properties of C2/m-20 carbon have been systematically investigated in this paper. The elastic constants and phonon spectra calculations show that C2/m-20 carbon is mechanically stable and dynamically stable at 0 GPa and 100 GPa. From our calculations, we found that C2/m-20 carbon has a larger bulk modulus of 412 GPa, a larger shear modulus of 463 GPa, a larger Young’s modulus of 1010 GPa, and a hardness of 70.6 GPa, which means that it is a superhard material with potential technological and industrial applications. C2/m-20 carbon exhibits greater anisotropy than C2/m-16 carbon and M-carbon using Young’s modulus and the universal anisotropic index. In addition, C2/m-20 carbon is an indirect and wide semiconductor with a band gap of 5.10 eV. The most extraordinary thing is that the band gap increases with increasing pressure.