The structural stability and the electronic properties of two-dimensional monolayer BC2N are studied by employing the first principles method based on the density functional theory. 16 polymorphic structures of monolayer BC2N are calculated. Analysis of the 16 band structures suggests that the structure with the highest symmetry is of a semimetal which is the same as graphene. All the other structures are of semiconductors with different band gaps, of which the most stable structure is of semiconductor with a direct gap of 1.63 eV. Based on the deformation charge density and the Bader analysis, the bonds CC, CN, CB, and BN in the most stable monolayer BC2N are mainly covalent, however, they present also significant ionic behaviors. Exerting a stress on the monolayer BC2N sheet changes the band gap, showing that the band gap increases during the compression while decreases during the stretch, and the system keeps a direct semiconductor.