In this study, three stable two-dimensional beryllium diphosphide (2D-BeP2) structures with the wrinkle and planar monolayers, namely MoS2-like 6[combining macron]m-BeP2 phase (1H-BeP2), pentagonal 4[combining macron]2m-BeP2 (Penta-BeP2) and planar mm2-BeP2 (Planar-BeP2), have been successfully predicted through the first-principles calculation combined with a global structure search method. The structural stabilities, mechanical properties, electron properties and superconductivities are also systematically investigated. Results indicated that the 2D MoS2-like 1H-BeP2 showed higher stability than the Penta- and Planar-BeP2 structures. The 1H-BeP2 structure possessed an intrinsic metallic characteristics with the bands crossing the Fermi level. Notably, the Penta-BeP2 is a typical semiconductor, and the planar-BeP2 is semi-metal with Dirac corn. Based on the calculation results of the electron properties, phonon properties and electron-phonon coupling (EPC), the layer 1H-BeP2 sheet is a phonon-mediated superconductor with a critical temperature (Tc) of about 1.32 K.