The application of biological mathematical theory to the studies of ecological balance and sustainable development is a hot topic of ecosystem.In marine fisheries catch process,not only is it necessary to ensure the ecological balance,but also to maximize the biggest fishing benefits,an important issue which marine fisheries concern the most.At present,there are few researches on the catch of small discrete systems.By applying the stability theory of discrete differential equations,we attempt to discuss the species with harvesting discrete Leslic predator-prey system and obtain the sufficient conditions of the existence and partial stability of positive equilibrium point.By constructing the Lyapunov function and employing the Taylor expanding of quadratic function,we find that if the positive equilibrium exists,the system is globally and asymptotically stable.With the extreme value method,we explore the optimal harvesting strategy under the premise of maintaining the stable harvesting so as to get the optimal economic returns.Finally,the feasibility of the main results is proved by one suitable example together with its numerical simulations.The findings can provide a theoretical basis and guidance significance for actual production.