The purpose of this paper is to study on migration and immigration of prey-predator with limited resources for both the species. The system comprises of a prey (S1), a predator (S2) that survives upon S1 with migration of prey and immigration of predator. The model equations of the system constitute a set of two simultaneous first order non-linear ordinary differential equations. The system would be stable if all the characteristic roots are negative, in case they are real, and have negative real parts, in case they are complex. All the four equilibrium points are identified and their stability discussed. The trajectories of solution curves for the equilibrium points are established. The global stability of linearized equations can be discussed by constructing a suitable Liaupnov's function. Further, the Runge-Kutta fourth order technique is used to compute the numerical solutions for the growth rate equations.