The nonradiative charge-transfer cross sections for protons colliding with Rb(5s) atoms are calculated by using the quantum-mechanical molecularorbital close-coupling method in an energy range of 10−3 keV–10 keV. The total and state-selective charge-transfer cross sections are in good agreement with the experimental data in the relatively low energy region. The importance of rotational coupling for chargetransfer process is stressed. Compared with the radiative charge-transfer process, nonradiative charge transfer is a dominant mechanism at energies above 15 eV. The resonance structures of state-selective charge-transfer cross sections arising from the competition among channels are analysed in detail. The radiative and nonradiative charge-transfer rate coefficients from low to high temperature are presented.