Summary: The bifurcation analysis for a Burgers mapping is studied. The existence and stability of the fixed points of this map are derived. Conditions of existence for pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The control of the map around stable Neimark-Sacker bifurcation is achieved by using the feedback polynomial controller technique. The complex dynamics, bifurcations and chaos are displayed by numerical simulations.