Abstract:We consider a Leslie-Gower predator prey model with additional food for predators. Here we investigate the dynamics of the model such as the permanence, determination of equilibrium points and their existence condition as well as their stability properties. It is shown that the model is permanence and has four equilibrium points, i.e., the extinction of both prey and predator point, the extinction of prey point, the extinction of predator and the coexistence point. The point of prey extinction and the coexistence point are conditionally stable while two other equilibrium points are always unstable. It is also shown that the additional food for predators may destabilize the extinction of prey point and at the same time stabilize the coexistence point. Such dynamical behavior agrees with our numerical results.