Abstract: A mathematical model is constructed to study the biological control of aphid population. Firstly, considering the periodic impulsive releases of its natural enemy seven-spot ladybird in the laboratory, the generalized logistic population dynamical model with growth stage of aphid is established. In order to distinguish the predation ability of ladybugs at different ages, a class of piecewise discontinuous functions are introduced into the system. Then, by using the fixed point theorem, conditions for the existence of positive periodic solutions of the system are found for various release strategies. Finally, with the help of numerical simulations, it is proved that the aphid population can be extinct by increasing the release rate of seven-spot ladybird in different cases.