The nonradiative charge-transfer processes for the Be3+(1s) + H(1s) collisions are investigated by the quantum-mechanical molecular orbital close-coupling method in the energy range of 0.01-10 keV/u. The radiative charge-transfer cross sections are calculated by the optical potential and semiclassical methods in the energy range 10(-6)-10(3) eV/u. The needed molecular data are obtained by the ab initio multireference single-and double-excitation configuration interaction method. Total and state-selective cross sections are presented and compared with other available theoretical data. Our calculation agrees well with the atomic orbital close-coupling results of Liu et al. [L. Liu, D. Jakimovski, J. G. Wang, and R. K. Janev, J. Phys. B 43, 144005 (2010)], but there exist some discrepancies with the semiclassical molecular orbital close-coupling results of Shimakura [N. Shimakura, J. Phys. B 21, 2485 (1988)]. The present results show that the capture to Si2+(1s3l) states is dominant in the whole energy range with the exception of a narrow range of 2-4 keV/u. Rotational couplings play an important role not only in the state-selective cross sections, but also in the total charge-transfer results. At energies below 40 eV/u, the radiative charge transfer exceeds the nonradiative process.