Discuss the dynamic properties of a class of discrete predator-prey models, and analyze the discrete system corresponding to the model by using polynomial complete discriminant system and central manifold theorem. The topological classification of the fixed points of the model was given by the polynomial complete discrimination system, and the parameter conditions for the fixed points in non-hyperbolic cases were found. By using central manifold theorem proves that the model undergoes transcritical and flip bifurcations near fixed points. The correctness of the above results was further verified through numerical simulation, and the corresponding Laypunov exponent was provided to demonstrate that the model produces chaotic phenomena under certain parameter conditions. The research results show that the model under discussion can generate dynamic properties such as transcritical bifurcatin, flip bifurcation, and chaos under certain parameter conditions.