In this paper, we explore the bifurcation analysis of a discrete-time predator-prey model in the interior of R_+^2. It is investigated that model has two boundary equilibria: O(0,0),A(1,0) and the unique positive equilibrium point B(r/(a+r),r/(a+r)). We studied the topological classification about equlibria: O(0,0),A(1,0) and B(r/(a+r),r/(a+r)) of the discrete-time model by utilizing method of Linearization. It is investigated that about A(1,0), predator population become extinction while prey undergoes a period-doubling bifurcation to chaos by taking r as bifurcation parameter. It is also investigated that model undergoes a Neimark-Sacker bifurcation in a small nbhd of B(r/(a+r),r/(a+r)) and in the meantime closed stable curve appears. In the perspective of biology, these curves correspond to periodic or quasi-periodic oscillations between predator and prey populations. Finally theoretical results are verified numerically.

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