A predator-prey model with stage structure is discussed. Based on the comparison principle for parabolic equations, the global existence of solutions and the global asymptotical stability of a semitrival solution are obtained. For the corresponding steady-state problem, a prior estimate of positive solution and a nonexistence result for non-constant positive solution are given. By using the bifurcation theorem, it is proved that the local bifurcation occurs at the three constant solutions in one dimension case, and the structure of solutions near the bifurcation point and the existence of non-constant positive solutions are discussed.

predator-prey； bifurcation theory； stage structure