A predator-prey model incorporating a prey refuge is discussed under homogeneous Neumann boundary conditions. First,the asymptotically stability of constant positive steady-solution and the prior estimate of positive steady-solution are given. Furthermore, the non-existence of non-constant positive solution is analyzed. In the end, the condition of existence of non-constant positive solution is given by the degree theory.%讨论了一类食饵具有避难所的捕食-食饵模型,其边界条件为齐次Neumann边界条件.首先分析了正常数平衡解的渐近稳定性,给出了正解的估计；其次,讨论了非常数正解的不存在性；最后,利用拓扑度理论,给出非常数正解存在的充分条件.
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