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The isotopic bare ion 13C6+ was employed to collide with helium at 4.15-11.08keV/u. The relative partial cross sections were measured by position-sensitive and time-of-flight coincident techniques. It is shown that the direct-ionization (DI) process can be completely ignored in this region, the transfer ionization (TI) process is the most important double-electron channel, and the probability of the pure double-electron capture (DC) process is quite small. The cross-section ratio of the total double-electron (DE) process (i.e. DC+TI) to the single-electron capture (SC) process is experimentally determined to be approximately a constant of 0.09 ± 0.03 in this region,and this value is obviously smaller than the predictions of the classical over-barrier models and the semi-empirical scaling laws. It is found that the cross-section ratio of pure DC to DE decreases obviously as the projectile velocity increases. Because the pure DC process only comes from the radiation de-excitation following the DC process and are competed by the TI process (comes from the auto-ionization following the DC process), this implies that the population of the two captured electrons depends distinctly on the collision velocity. Comparison with works on Ar16+-He by Wu et al. [Phys. Rev. A 48 (1993) 3617] reveals that the strong projectile-dependent character of the pure DC process exists.