In this paper, we will investigate the existence of positive solutions to the predator-prey interacting system $$ {-varphi(x, u)Delta u = uf(x, u, upsilon) in Omega {-psi(x, upsilon)Deltaupsilon = upsilon g(x, u, upsilon) {frac{partial n}{partial u} + ku = 0 on partialOmega {frac{partial n}{partialupsilon} + sigmaupsilon = 0. $$ in a bound region $Omega$ in $R^n$ with smooth boundary, where $varphi$ and $psi$ are strictly positive functions, serving as nonlinear diffusion rates, and $k, sigma > 0$ are constants.