Abstract A method for calculating the dynamic response of the diffusion-reaction system with prey and predator model is proposed by using superposition of normal modes. For this kind of nonlinear equation with N-Degrees of Freedom (DOF) discretized by finite element method (FEM), mode superposition is used to evaluate the transient process of the system subjected to initial conditions. For the calculation of the generalized coordinates in vectors of superposition, the fourth-order Runge-Kutta method is employed to solve the ordinary differential equations of the N-DOF system. The results obtained are compared with those by three-step explicit FEM. Two of methods can predict the oscillation phenomena in prey and predator in two-dimensional space.