Abstract: In this paper,we investigate a dynamical properties of a Monod-Haldane type predator-prey system with nonzero constant prey harvesting.The system exhibits numerous kinds of bifurcation phenomena,including the Saddle-node bifurcation,the Bogdanov-Takens bifurcation,the subcritical and supercritical Hopf bifurcation.Moreover,we give some numerical simulations to illustrate the obtained results.This may enrich the dynamics in harvesting predator-prey system.