In this paper, a modified Leslie-Gower predator-prey model with strong Allee effect and double harvesting was studied analytically and numerically. The aim of the research is to provide an understanding of the impact of harvesting on the predator-prey model. The existence and stability of the equilibria was discussed, and we analyzed the existence of some bifurcations, such as saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. Furthermore, some numerical simulations were proposed to illustrate the dynamics of the model. Numerical results are consistent with the analytical results.