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The nonlinear dynamic characteristics of traffic flow based on continuous car-following model were studied in this paper. Discrete Bierley car-following model was transformed into continuous nonlinear dynamic model with nonintegral dimension in difference method and solved in averaging method. Stability and bifurcation characteristics were analyzed, and time histories and phase diagrams of this system were obtained in simulation. The results of analysis shows that bifurcation appears in the system with the variation of system parameters, and it is helpful for the stability of traffic flow to keep velocity of vehicle from violent variation and enhance the reaction sensitivity of driver. The results are useful to management and control to traffic flow.