By means of perturbation theory and bifurcation theory,a predator-prey model between two species with functional response subject to homogeneous Neumann boundary conditions is studied.The localb-ifurcation at positive constant steady-state solution (u^*,v^*) is obtained by treating diffusion coefficient as the bifurcation parameter.Moreover,the structure of the solut ion near bifurcation points is given and the local branch can be extended to global branch.