Using CALYPSO crystal structure prediction method via particle swarm optimization, we found a novel tetragonal BC2N with the space groupI4/MMM. The band structure, electronic density of states, elastic constants, and bulk modulus of BC2N carbon were investigated using first principles calculations based on density functional theory. The present results reveal that BC2N is dynamically stable, and simultaneously posses a high bulk modulus of 3544 GPa and a high shear modulus of 3755 GPa. Furthermore, the electronic structure calculations show that it is a direct semiconductor with a band gap of 216 eV, and the Vickers hardness value of I 4 carbon is 656 GPa. The results adequately indicate that BC2N maybe a potential superhard material. Our work may provide some theoretical guidance toward exploring novel superhard materials.