Alpha–proton differential flow (V α p ) of coronal mass ejections (CMEs) and solar wind from the Sun to 1 au and beyond could influence the instantaneous correspondence of absolute abundances of alpha particles (He2+/H+) between the solar corona and interplanetary space as the abundance of a coronal source can vary with time. Previous studies based on Ulysses and Helios showed that V α p is negligible within CMEs from 5 to 0.3 au, similar to slow solar wind (<400 km s−1). However, recent new observations using Parker Solar Probe (PSP) revealed that the V α p of slow wind increases to ∼60 km s−1 inside 0.1 au. It is important to answer whether the V α p of CMEs exhibits similar behavior near the Sun. In this Letter, we report the V α p of a CME measured by PSP at ∼15 R ⊙ for the first time, which demonstrates that the V α p of CMEs is obvious and complex inside 0.1 au while keeping lower than the local Alfvén speed. A very interesting point is that the same one CME duration can be divided into A and B intervals clearly with Coulomb number below and beyond 0.5, respectively. The means of V α p and alpha-to-proton temperature ratios of interval A (B) is 96.52 (21.96) km s−1 and 7.65 (2.23), respectively. This directly illustrates that Coulomb collisions play an important role in reducing the nonequilibrium features of CMEs. Our study indicates that the absolute elemental abundances of CMEs also might vary during their propagation.