In order to study the impact of cooperative behaviors between predators on the dynamic behavior of the food chain system, a top-level predator (which only feeds on the predator population) on the basis of the original cooperative hunting model is introduced, and a food chain model with cooperative hunting is established. The local stability of the equilibrium point is discussed by using the linearization method. By establishing an appropriate Lyapunov function, a sufficient condition for the global stability of the system at the equilibrium point is given. In addition, by using the central manifold reduction theorem, the explicit formulas of the branch periodic solution is studied. Numerical simulations are conducted to verify our theoretical analysis. The results show that when there is no cooperative relationship between predators, the positive equilibrium point is stable. With the increase of cooperative predation parameter \alpha, the system will have a stable limit cycle, and the limit cycle will continue to expand following the increase of cooperative predation parameter \alpha. Moreover, if the predator population density is too large, the system will produce continuous periodic oscillation, that is, the three species i.e. diet, mid-level predator, top-level predator, either coexist in the form of periodic oscillation, or the number of species eventually tends to be stable. Therefore, cooperative hunting is more conducive to maintaining ecological balance.