A delayed biological model of predator-prey interaction with stage structure is investigated. It is assumed that the prey population has two stages, immature and mature. The immature prey suffers the death risk in the process of growing into mature prey. The growth of the predator is affected by the time delay due to gestation. By some lemmas and methods of delay differential equation, the conditions for the permanence, existence of positive periodic solutions and extinction of the system are obtained. Numerical simulations are presented that illustrate the analytical results as well as demonstrating certain biological phenomena. In particular, overcrowding of the predator does not affect the permanence of the system, but our numerical simulations suggest that overcrowding reduces the density of the predator.

permanence, periodicity, extinction, stage structure.