The nonradiative charge-transfer processes of Be3+(1s)/B4+(1s) colliding with He(1s2) are investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method from 10 eV/u to 1800 eV/u. Total and state-selective cross sections are obtained and compared with other results available. Although the incident ions have the same number of electrons and collide with the same target, their cross sections are different due to the differences in molecular structure. For Be3+(1s) + He(1s2), only single-electron-capture (SEC) states are important and the total cross sections have a broad maximum around E = 150 eV/u. While for B4+(1s) + He(1s2), both the SEC and double-electron-capture (DEC) processes are important, and the total SEC and DEC cross sections decrease rapidly with the energy decreasing.