The present paper deals with the problem of non-selective harvesting of a prey-predator system in which both the prey and the predator species obey the law of logistic growth and each predators functional response to the prey approaches a constant as the prey population increases. Boundedness of the exploited system is examined. The existence of its steady states and their stability are studied using eigenvalue analysis. The existence of bionomic equilibria has been considered. The problem of determining the optimal harvest policy is then solved by using Pontryagin's maximal principle. Finally, some numerical examples are given to illustrate the results. (Contains 2 figures.)