The ionization process in the collisions of He2+ with Cq+ (q = 0-5) is investigated by using the continuum-distorted-wave eikonal-initial-state approximation. Double-differential cross sections for 1s and 2s sub-shells are obtained at the electron-ejected angle Σ = 0° with the projectile energy ranging from 30 keV/u to 10 MeV/u.Variation of ionization mechanisms with q in Gq+ is studied, and the dependences on the projectile energies and target sub-shells are also discussed. It is found that in the whole energy range, the absolute values of soft collision (SC) and binary encounter (BE) peaks decrease with increasing q. For the lower incident energies, the electron capture to the projectile continuum (ECC) peak decrease with increasing q as well as SC and BE peaks. For the higher incident energies (＞ 1 MeV/u), the absolute value of ECC peak increases with increasing q, so that the crossings of cross sections appearfor Gq+ with different q. This can be explained by the matching of velocities between the projectile and the electron initially bound to the target.