In　this　paper,　a　four-species　food　web　model　is　formulated　to　investigate　the　influence　of　fear　effect　and　nonlinear　top　predator　harvesting　on　the　dynamical　behaviors.　The　global　stability　of　the　system　at　the　interior　equilibrium　is　explored　by　Li–Muldowney　geometric　approach.　By　applying　the　Sotomayor＇s　theorem,　it　is　shown　that　the　system　undergoes　transcritical　bifurcation　and　pitchfork　bifurcation.　The　conditions　for　the　occurrence　of　Hopf　bifurcation　are　established,　and　the　stability　of　the　bifurcating　limit　cycle　is　discussed　by　normal　form　theory.　Finally,　the　numerical　simulations　are　carried　out.　It　is　observed　that　the　system　presents　chaotic　dynamics,　periodic　window　and　chaotic　attractors.　Two　distinct　routes　to　chaos　are　discovered,　one　is　period　doubling　cascade　and　the　other　is　the　generation　and　destruction　of　quasi-periodic　states.　Moreover,　it　is　found　that　the　fear　effect　can　suppress　fluctuations　in　population　density　to　stabilize　the　system.　©　2024　International　Association　for　Mathematics　and　Computers　in　Simulation　(IMACS)