By using the global analytical method,the magnetic field distribution and electromagnetic torque of the concentric magnetic gear are analyzed and calculated.On this basis,the optimization design is carried out by using the genetic algorithm in optimization toolbox of Matlab（GAOT）.The experiment results show that the optimization design method of the concentric magnetic gear based on Matlab genetic algorithm toolbox is practicable and effective and a new approach for the analysis and design of the concentric magnetic gear is provided.It is significant for the research and application of the concentric magnetic gear.