In　this　paper,　a　discrete　Leslie-Gower　predator-prey　system　with　Michaelis-Menten　type　harvesting　is　studied.　Conditions　on　the　existence　and　stability　of　fixed　points　are　obtained.　It　is　shown　that　the　system　can　undergo　fold　bifurcation,　flip　bifurcation,　and　Neimark-Sacker　bifurcation　by　using　the　center　manifold　theorem　and　bifurcation　theory.　Numerical　simulations　are　presented　to　illustrate　the　main　theoretical　results.　Compared　to　the　continuous　analog,　the　discrete　system　here　possesses　much　richer　dynamical　behaviors　including　orbits　of　period-16,　21,　35,　49,　54,　invariant　cycles,　cascades　of　period-doubling　bifurcation　in　orbits　of　period-2,　4,　8,　and　chaotic　sets.