<p>The delayed fear of prey towards predator and delayed gestation of predator usually affect the system dynamical behaviors. On the other hand, additional food supplement is a commen measure for people to preserve species from extinction and keep natural balance for continuous development in system control. Thus in this paper, we construct a predator-prey model with predator induced fear, additional food, Holling-II type functional response and time delays, and then generalize it to the random environment. Next, we establish some criteria of the asymptotical stability of equilibrium state, and stationary distribution for stochastic case. Considering the impacts of fear, additional food and time delays, we analyze the Hopf bifurcation of them. Finally by some numerical examples and graphical analysis, we intuitively validate such properties as stability, instability and Hopf bifurcation. Our findings reveal the significant impacts of fear, additional food and time delays on the system stability.</p>