A three-dimensional stage-structured predator-prey model is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with non-constant harvesting. Time lag in maturation of the predator is introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a supercritical Hopf bifurcation when the maturation time lag crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.