The solution to the job shop scheduling problem (JSSP) is of great significance for improving resource utilization and production efficiency of enterprises. In this paper, in view of its non-deterministic polynomial properties, a multi-agent genetic algorithm based on tabu search (MAGATS) is proposed to solve JSSPs under makespan constraints. Firstly, a multi-agent genetic algorithm (MAGA) is proposed. During the process, a multi-agent grid environment is constructed based on characteristics of multi-agent systems and genetic algorithm (GA), and a corresponding neighbor interaction operator, a mutation operator based on neighborhood structure and a self-learning operator are designed. Then, combining tabu search algorithm with a MAGA, the algorithm MAGATS are presented. Finally, 43 benchmark instances are tested with the new algorithm. Compared with four other algorithms, the optimization performance of it is analyzed based on obtained test results. Effectiveness of the new algorithm is verified by analysis results.