Charge transfer in collisions of Si4+ ions with He atoms below 100 keV/u is studied by using a molecular orbital representation within both the semiclassical and quantal representations. Single transfer reactionSi4+ + He → Si3+ + He+ has been studied by a number of theoretical investigations. In addition to the reaction (1), the first semiclassical MOCC calculations are performed for the double transfer channelSi4+ + He → Si2+ + He2+Nine molecular states that connect both with single and double electron transfer processes are considered in the present model. Electronic states and corresponding couplings are determined by the multireference single- and double- excitation configuration interaction method. The present cross sections tie well with the earlier calculations of Stancil et al., Phys. Rev. A 55, 1064 (1997) at lower energies, but show a rather different magnitude from those of Bacchus-Montabonel and Ceyzeriat, Phys. Rev. A 58, 1162 (1998). The present rate constant is found to be significantly different from the experimental finding of Fang and Kwong, Phys. Rev. A 59, 342 (1996) at 4,600 K, and hence does not support the experiment.