The Decision-Making (DM) problem is investigated for Cooperative Multiple Target Attack in air combat. It is to find a proper assignment of M friendly fighters to N hostile fighters in order to achieve the optimal expected attack effect according to the air combat situation. In this paper, the DM problem is formulated mathematically and then a Hybrid Adaptive Genetic Algorithm (HAGA) is presented for solving it. In the HAGA, a local search approach is embedded into the Adaptive Genetic Algorithm (AGA) to improve its search performance. In addition, an unconventional crossover operator is given to meet the constraints of the DM problem. Simulation experiment results show that the HAGA is more effective to solve the DM problem than the AGA.