A　Lotka–Volterra　predator–prey　system　incorporating　fear　effect　of　the　prey　and　the　predator　has　other　food　resource　is　proposed　and　studied　in　this　paper.　It　is　shown　that　the　trivial　equilibrium　and　the　predator　free　equilibrium　are　both　unstable,　and　depending　on　some　inequalities,　the　system　may　have　a　globally　asymptotically　stable　prey　free　equilibrium　or　positive　equilibrium.　Our　study　shows　the　fear　effect　is　one　of　the　most　important　factors　that　lead　to　the　extinction　of　the　prey　species.　Such　a　finding　is　quite　different　from　the　known　result.　Numeric　simulations　are　carried　out　to　show　the　feasibility　of　the　main　results.　©　2020,　The　Author(s).