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In this paper, we focus on smooth periodic wave, periodic blow-up wave, solitary wave, blow-up wave, kink and anti-kink wave solutions for a modified Broer-Kaup system. Based on the approach of dynamical systems, the existence of above traveling waves is proved and their all possible exact parametric representations are presented. When the energy of Hamiltonian system corresponding to this system varies, we also show the convergence of the periodic wave solutions. Along with the details of the analysis, the analytical results lastly are numerical simulated. Keywords: A modified Broer-Kaup system, Dynamical behaviors, Nonlinear wave, Exact solution