Carbon fiber braids are widely applied in various industrial fields as structural components. However, using braiding machines to braid carbon fibers is an emerging technology, but some technical problems must be solved. For instance, carbon fibers are easily fluffed when using traditional carriers; with increasing braiding speed, the machine fiercely vibrates. To investigate these problems, an improved mechanical structure of the carrier is designed, which reduces the friction between the carbon fiber and guide hole and changes the carbon fiber storage quantity. Based on the carrier, the corresponding mathematical model of the tensioning system is established by the dynamical equations, and numerical analyses and simulations are carried out. Moreover, the validation of the established mathematical model is verified. According to the results of the simulation, the fluctuation in the tensioning force is smaller than that in previous studies, and the trend is in accordance with previous research results. As a result, the present model provides a better description of the dynamic process of carbon fiber braiding.