In　this　paper,　we　consider　a　predator–prey　model　with　Allee　effect,　fear　effect　and　prey　refuge.　By　considering　the　prey　refuge　as　a　parameter,　we　give　the　threshold　condition　for　the　stability　of　the　system,　and　prove　that　the　system　undergoes　a　supercritical　Hopf　bifurcation.　We　show　that　increasing　the　prey　refuge　or　Allee　effect　can　make　the　dynamical　behavior　of　the　system　more　complicated;　the　fear　effect　or　Allee　effect　has　no　influence　on　the　prey　density,　but　can　lead　to　a　decrease　of　the　predator　population　at　positive　equilibrium.　©　2020,　The　Author(s).