We focus on the dynamical characters for a topological superconductor model. Considering a chiral p-wave superconductor with open and periodic boundary conditions in orthogonal directions, we show the bulk-boundary correspondence comparing to the topological phase diagram by Pfaffian. The expectations of Pauli matrixes are used to reflect the topological phase for this model. The dynamical quantum phase transition revealed by quench does occur in the parameter region consistent with the topological phase diagram. Besides quenching, temporal dynamical non-analyticities occur until the parameter crossing the topological critical point slowly. And the dynamics of the excitation behave differently in different topological phases. The dynamical phase transition behaves robustly against noise during evolution until the amplitude of noise reaching a threshold with the time-Anderson localization dominates. This work manifests the topological phase can be detected in a dynamical way.