The potential energy curves of X1Σ+, A1Σ+, C1Σ+, and B1Π are calculated with high-level MRDCI method, and the calculated spectroscopic constants of those states are in good agreement with most recent experimental data. On the basis of high precision PECs, the radiative processes of H+ + Be collisions are studied by using the fully quantum, optical potential and semiclassical methods in the energy ranges of 10−8 eV/u–0.1 eV/u, and the radiative decay, the radiative charge transfer, and the radiative association cross-sections are computed. It is found that the radiative association process is dominant in the energy region of 10−8 eV/u–0.02 eV/u, while radiative charge transfer becomes important at higher energies. Rich resonance structures are present in the radiative association and charge transfer cross-sections in the whole energy region considered, which result from the interaction between the quasi-bound rovibrational (J, v) states in the entrance channel with the final continuum state. Significant isotope effects have been found in the radiative decay processes of H+ + Be collisions.