In order to study target assignment problems of multi-ground-to-air-missile-weapon-system to multi-aggressive-target, the factor of overlapping shooting-area is considered, wreathe status's changes of different shooting-areas to different aggressive targets are analyzed, and the target assignment progress is also fractionized. The best assignment method is found out through shooting-value's comparison between sub-zones. On the basis of the above,a genetic algorithm based on predatory search strategy (PSGA) is designed. The simulation results shows that the model and the algorithm are feasible.