AbstractIn this paper, a new density‐dependent host–parasitoid model is proposed. The modification is based on density‐dependent factor by introducing Hassell growth function in host population. Moreover, the permanence of solutions, existence and uniqueness of positive equilibrium, local asymptotic stability and global behavior of the positive equilibrium point are also investigated. It is demonstrated that system endures Neimark–Sacker bifurcation for wide range of bifurcation parameter. In order to control chaos due to emergence of Neimark–Sacker bifurcation, two feedback control strategies, that is, OGY and hybrid control methods are implemented. Finally, all mathematical analysis, particularly, Neimark–Sacker bifurcation, chaos control strategies, and global asymptotic stability of unique positive point are verified with the help of numerical simulations.