Abstract: Considering that the birth rate and mortality rate of the pest population and the human control for the pest keep a periodic variation, a non-autonomous pest control model combined with chemical control and biological control was established. Further, regarding the pesticide function as a piecewise-continuous exponential functions, the residual effects of pesticides have been introduced to the pest control model, and the sufficient condition of the global asymptotic stability for the pest-eradication periodic solution was given.