In　ecosystems,　hunting　cooperation　of　the　predator　will　intensify　the　survival　pressure　faced　by　the　prey,　and　then　promote　anti-predator　behavior　in　the　prey　population.　Therefore,　it　is　of　biological　significance　to　study　the　prey＇s　anti-predator　behavior　and　the　predator＇s　hunting　cooperation　simultaneously.　In　this　paper,　a　mathematical　model　that　encompasses　both　aspects　is　developed.　Through　rigorous　and　comprehensive　analysis　of　equilibria　and　bifurcation　phenomena,　this　study　reveals　how　these　two　behaviors　influence　population　dynamics　and　ecosystem　stability.　In　detail,　as　the　hunting　cooperation　parameter　a　increases,　the　density　of　the　prey　population　decreases.　When　a　is　extremely　large　or　small,　it　will　hinder　the　persistence　of　predator　and　prey　populations,　and　only　moderate　hunting　cooperation　can　maintain　the　ecosystem　balance.　Furthermore,　moderate　anti-predator　behavior　of　the　prey　can　suppress　predators＇　hunting　efficiency,　while　once　the　anti-predator　behavior　exceeds　a　critical　threshold,　it　will　disrupt　the　coexistence　of　predator　and　prey　populations.　The　findings　in　this　research　can　be　viewed　as　an　improvement　and　a　complement　to　those　with　anti-predator　behavior　or　hunting　cooperation.