We　proposed　and　analyzed　a　predator-prey　model　with　both　the　additive　Allee　effect　and　the　fear　effect　in　the　prey.　Firstly,　we　studied　the　existence　and　local　stability　of　equilibria.　Some　sufficient　conditions　on　the　global　stability　of　the　positive　equilibrium　were　established　by　applying　the　Dulac　theorem.　Those　results　indicate　that　some　bifurcations　occur.　We　then　confirmed　the　occurrence　of　saddle-node　bifurcation,　transcritical　bifurcation,　and　Hopf　bifurcation.　Those　theoretical　results　were　demonstrated　with　numerical　simulations.　In　the　bifurcation　analysis,　we　only　considered　the　effect　of　the　strong　Allee　effect.　Finally,　we　found　that　the　stronger　the　fear　effect,　the　smaller　the　density　of　predator　species.　However,　the　fear　effect　has　no　influence　on　the　final　density　of　the　prey.　©　2020　by　the　authors.