The crystal structure, mechanical anisotropy, elastic properties and electronic characteristics, as well as the stability, of P4/m BN are predicted by means of density functional theory. In this work, BN in the P4/m phase demonstrates mechanical and dynamical stability. Compared with the values of bulk B, E and G in the P4/m phase, the B of BN in the P4/m phase is greater than that of dz4 BN, while the G and E of P4/m BN are greater than those of Pnc2 BN and dz4 BN. The ratio of the bulk-to-shear modulus for P4/m BN is less than 1.75 and dz4 BN, dz2 BN and lzlz2 BN, indicating that P4/m BN is more brittle than dz4 BN, dz2 BN and lzlz2 BN. P4/m BN exhibits stronger mechanical anisotropy in G and E than Pbca BN, P42/mnm BN and Pm-3m BN but much weaker mechanical anisotropy than P4/mbm BN, B7N7, B11N11 and B15N15. In addition, P4/m BN is a quasi-direct bandgap semiconductor, and the difference between the direct and the indirect bandgap is 0.008 eV. In order to obtain further characteristics of P4/m BN for future synthetic verification, the X-ray diffraction (XRD) patterns for P4/m BN are also calculated. Given its properties, P4/m BN is a good candidate for photoelectric devices.