A new co-evolutionary genetic algorithm is proposed. Based on the coevolution idea, the algorithm divides the population into groups. Each group adopts different crossover and mutation strategies according to the individual situation and difference in its own group. To prevent prematurity, this algorithm only employs the adaptive strategy to dynamically adjust the mutation factor when the catastrophic condition is not triggered. When the catastrophic condition is triggered, with the adaptive strategy applied, the catastrophe mechanism is introduced to generate some new individuals to jump out of the local optimum. The results of function optimization show the effectiveness of the algorithm. The algorithm is used to deal with flow shop scheduling with the optimization objective of minimizing the maximum completion time. The results show that the algorithm is superior to the traditional genetic algorithm in convergence speed and accuracy of optimization results and performs well in solving the shop scheduling problems.