The dynamical behavior of a predator-prey model with additional food inducing competition among predators incorporating anti-predator behavior is analyzed in this paper. The existence, stability, and local dynamics of the equilibria are discussed. By using bifurcation theory, we studied the existence of Hopf bifurcation and Bogdanov-Takens bifurcation. The numerical simulations are presented to illustrate the results of the theoretical analysis, and complex dynamical behaviors were found, such as limit cycles and homoclinic cycles.