Abstract: A predator-prey model with strong Allee effect of prey is considered. Firstly, by use of the linearization method, the stability of the positive equilibrium is proved; Then, a priori estimate of solutions of corresponding steady-state problem is given by the maximum principle and the Harnack inequality; Finally, the nonexistence and existence of non-constant positive solutions are established by the energy integration and the topological degree theory, respectively. The result shows that the predator and prey can coexist when the prey’s Allee effect is controlled reasonably.