Abstract: The dynamics of a predator-prey system consisting of two competitive prey populations and one predator population, which feeds on both the prey species, were studied. Firstly,  the positivity and boundedness of the solutions and the existence of all the possible equilibria of this system were investigated. Further, by using qualitative method of ordinary differential equation, the local asymptotically stability of equilibria and the persistence of the system were discussed. The global asymptotic stability of the positive equilibrium was obtained by constructing Lyapunov function. Finally, the numerical analyses were given to show the effectiveness of the main results.