<p>In this paper, a quad-trophic food chain model with Beddington–DeAngelis functional response is formulated by incorporating fear effect and prey refuge. Firstly, it is proved that the system is dissipative. Five types of equilibria are identified, and the criteria for local and global stabilities of the coexistence equilibrium are deduced by Routh–Hurwitz criteria and Li–Muldowney geometric approach. Secondly, multiple bifurcations are explored. It is shown that the system undergoes transcritical bifurcation and pitchfork bifurcation by the Sotomayor’s theorem, Hopf Bifurcation by normal form theory, heteroclinic bifurcation and homoclinic bifurcation by stability analysis of manifolds. Moreover, we present numerical experiments to verify the correctness of theoretical analysis. In particular, it is observed that the system undergoes period doubling and period halving cascades, cataclysm, and quasi periodic bifurcation (a torus), thereby entering or escaping chaotic state. It is also observed a saddle-focus homoclinic loop, a period two saddle-focus homoclinic loop, and a period three saddle-focus homoclinic loop for the system. Finally, it is found that fear effect and prey refuge can stabilize the system.</p>