In this paper, we consider an ecological model consisting of prey and predator along with special effect of diffusion and random perturbations. The Routh-Hurwitz principle and Lyapunov’s function are employed to analyze the local and global stability of the system respectively, without delay and diffusion, around the positive equilibrium point. The stability of the system is analyzed with delay and without diffusion. Diffusive instability is also verified by perturbation technique and Routh-Hurwitz criteria. The analytical estimates of the meansquare fluctuation of population have also been calculated to explore the dynamics of the system in the presence of Gaussian additive white noise. Computer simulations through MATLAB have been carried out to illustrate the analytical results with suitable numerical examples. © RJPT All right reserved.