We study the local dynamics and bifurcations of a two-dimensional discrete-time predator-prey model in the closed first quadrant R 2 +. It is proved that the model has two boundary equilibria: O(0, 0), A(α 1-1 α 1 , 0) and a unique positive equilibrium B(1 α 2 , α 1 α 2-α 1-α 2 α 2) under some restriction to the parameter. We study the local dynamics along their topological types by imposing the method of linearization. It is proved that a fold bifurcation occurs about the boundary equilibria: O(0, 0), A(α 1-1 α 1 , 0) and a period-doubling bifurcation in a small neighborhood of the unique positive equilibrium B(1 α 2 , α 1 α 2-α 1-α 2 α 2). It is also proved that the model undergoes a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium B(1 α 2 , α 1 α 2-α 1-α 2 α 2) and meanwhile a stable invariant closed curve appears. From the viewpoint of biology, the stable closed curve corresponds to the periodic or quasi-periodic oscillations between predator and prey populations. Numerical simulations are presented to verify not only the theoretical results but also to exhibit the complex dynamical behavior such as the period-2,-4,-11,-13,-15 and-22 orbits. Further, we compute the maximum Lyapunov exponents and the fractal dimension numerically to justify the chaotic behaviors of the discrete-time model. Finally, the feedback control method is applied to stabilize chaos existing in the discrete-time model.