<p>In this paper, we consider a delayed prey–predator system with hunting cooperation. The dynamical behaviour of this model involving the hunting cooperation of predators in non-delayed and delayed cases is investigated. Here, we consider the functional response depending on both prey and predator densities. In the case of non-delayed and delayed models, we investigate the stability of coexisting equilibrium points and the existence of Hopf bifurcation, where the discrete delay is considered the bifurcation parameter in the delayed system. In delayed and non-delayed cases, the system exhibits very novel dynamics, including the co-dimension two bifurcation point i.e., the Bogdanov–Takens bifurcation point. The main focus of this work is to study the stabilizing role of maturation time delay for the delayed prey–predator model, deriving explicit conditions for the stability of interior equilibrium points for non-delayed and delayed models, along with the supporting numerical simulation to validate our investigated analytical results.</p>