Understanding of magnetic domain wall dynamic behavior is one of the important issues in the realization of spintronic device based on domain wall motion. We investigate the dynamic behaviors of the magnetic domain wall propagation in L-shaped ferromagnetic nanowires under external magnetic driving fields. By micromagnetic simulation, we observe a dynamic characteristic of the magnetic domain wall in a ferromagnetic nanowire with varying the external field. By changing the nanowire thickness, we examine the influence of the demagnetizing field from the nanowire surface on the domain wall dynamics under a magnetic driving field after Walker breakdown field. Using an auxilliary magnetic field perpendicular to the nanowires, we analyze the effect of the demagnetizing field on the domain wall dynamic behaviors. The results show that the stronger external field or the thicker nanowire can enhance the generation of the demagnetizing field on the nanowire surface, leading to the occurrence of the Walker breakdown phenomenon with the periodic change of the inner spin structure of the domain wall during the domain wall propagation in the nanowires. By using an auxilliary magnetic field perpendicular to the nanowires, we find that the strength and the direction of the demagnetizing field can be modulated. It implies that the dynamic behavior of domain wall propagation in the nanowire is controllable.