In natural world, many biological populations exist in a hierarchical structure which is similar to human societies, both the age and size of individual populations are important factors to influence the hierarchical structure of populations, and the dominance of the individual size in the hierarchical structure of biological populations has more pronounced and widespread. Therefore, based on the fact that individuals with larger size in a population have a greater advantage in obtaining food and reproducing offspring, this paper researches the existence of positive equilibria state and the stability of zero equilibria state of a nonlinear predator-prey model with hierarchical size-structured. A non-zero fixed point theorem is used to show that there is at least one positive equilibrium state in the model. The stability criterion of the zero equilibrium state is obtained by deriving the characteristic equation of the zero equilibrium state and constructing the Lyapunov function. Finally, present some numerical experiments of zero equilibrium state to verify the conclusions.