The dynamical behavior and traveling wave solutions of DegasperisProcesi equation were studied by using bifurcation theory of dynamical system and qualitative theory. Based on the character of integral system and exploiting the energy of Hamiltonian system, the phase portraits were plotted by using the Maple. The relation between the parameter and the type of different traveling wave solutions was revealed, the bifurcation values of different traveling wave solution were given, and the reason for peakon was shown. Under different parameter conditions, exact traveling wave solutions were also given. The numerical simulation shows the correctness of the theoretical analysis.