In this paper, the dynamical behaviors of a twodimensional discrete parabolic map are investigated in detail. Firstly, the existence and stability of fixed point of the map are cited as presented in［3］ that it has three fixed points and the sufficient conditions of their stability are obtained, respectively, when the parameter b changes. Secondly, sufficient conditions are derived for the existence of Fold bifurcation, Flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Finally, using numerical simulation, we verify the existence of the Fold bifurcation, the Flip bifurcation and the Hopf bifurcation of the map. Meanwhile, the complex symmetry breaking bifurcation phenomenon of the map is observed.