Abstract: Engineering vibration of the axially moving structure always has been one of the important topics in the field of dynamics.In order to analyze the vibration in the project more completely，this paper discusses in detail the vibration characteristics of the axially moving functionally graded Timoshenko beam under magnetic field. The dynamic equations and corresponding simply supported boundary conditions of the axially moving functionally graded Timoshenko beam under the magnetic field are obtained. The complex modal method is used to obtain the corresponding relation between the natural frequencies and the attenuation coefficients and the axial speeds with different parameters. The differential quadrature method is used to analyze the variation of the first four order natural frequencies and attenuation coefficients with axial speed under the magnetic field. The results are compared with those of the complex mode method. The results show that the solution obtained by the complex modal method is an exact analytical solution.The attenuation coefficient is asymmetrical and the coupling natural frequency is separable. As the axial speed，the magnetic field strength，and functional gradient index increase，the natural frequency decreases. The natural frequency increases with the increase of the support stiffness parameter.