In this talk, for a food chain model with general logistic source in high-dimensional space, it is proved that if the logistic source term satisfies appropriate conditions, then the classical solution exists globally and is bounded by means of important inequalities and heat semigroup theory. It is also concerned that the global dynamics of a food chain model with nonlinear diffusion. We first employ coupled estimate techniques and Moser iteration methods to show the global boundedness of solution if the exponents of nonlinear diffusion function satisfy appropriate conditions. When the parameters of model satisfy appropriate conditions, we then prove the asymptotic behavior of solutions by constructing different energy functional.