In this paper, the dynamical behaviors of a discrete-time prey-predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the model are analyzed. It is shown that the model can undergo a Neimark-Sacker bifurcation at the unique positive fixed point by choosing a as a bifurcation parameter. The conditions of the existence for Neimark-Sacker bifurcation and the direction of bifurcation via bifurcation theory are presented. Also, some numerical simulations are presented to support of the analytical finding. Then bifurcation diagrams and phase portraits of the model are given.