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讨论了齐次Neuman边界条件下具有Holling-III型响应函数的捕食-食饵模型的共存解的存在性。首先研究了反应扩散系统正常数解的线性稳定性；其次利用极值原理给出了解的先验估计；最后给出了平衡态系统非常数正解不存在性的条件。“,”In this paper, the coexistence of a predator-prey model subject to the homogeneous Neumann boundary condition with Holling type--III functional response is investigated. At first, the stability of the positive constant solution of the reaction diffusion systems is discussed. Secondly, give a priori estimates by use of the maximum principle. Then, the condition of the nonexistence of the nontrivial nonnegative solutions of the steady-state system is obtained.