A novel body-centered tetragonal CN2 (4 units per cell), named as bct-CN2, has been predicted here using our newly developed particle swarm optimization algorithm for crystal structure prediction. Bct-CN2 is energetically much superior (3.022 eV per f.u.) to previously proposed pyrite structure and stable against decomposition into a mixture of diamond + N2 or 1/3(C3N4 + N2) above 45.4 GPa. No imaginary phonon frequencies in the whole Brillouin zone indicate bct-CN2 is dynamically stable. The electronic calculations indicate that bct-CN2 is a wide gap dielectric material with an indirect band gap of 3.6 eV. The ideal tensile, shear, and compressive strength at large strains of bct-CN2 are examined to understand further the microscopic mechanism of the structural deformation. Strikingly, it is found that bct-CN2 has high calculated ideal strength, bulk modulus, shear modulus, and simulated hardness, indicating its very incompressible and superhard nature. The results provide new thoughts for designing and synthesizing novel superhard carbon nitrides, and insights for understanding the mechanical properties.