In this paper, after a continuous predator-prey model incorporating Allee effect and cannibalism is simplified, its discrete system is derived by using semidiscretization method. Not only the existence and local stability of fixed points of the discret system are investigated, but also, what's more important, the sufficient conditions for the occurrence of its period-doubling bifurcation and Neimark-Sacker bifurcation are also obtained by using the center manifold theorem and bifurcation theory. Finally some numerical simulations are given to illustrate the existence of Neimark-Sacker bifurcation.