<p>In this paper, the ratio dependent continuous model with Michaelis-Menten harvesting rate wasdiscretized using nonstandard finite difference scheme (NSFD). The new method preserves both thelocal stability of the equilibrium points and the positivity of the solutions. Also, the NSFD methodshows dynamic consistency with the proposed continuous predator-prey model. However, due tothe difficulty of solving such models, the behaviour of numerical solutions have been examined. Thephase portrait and solution graphics of the discretized model are shown.<br></p>