The axial velocity and the material’s heterogeneity introduce the great challenge on the vibration analysis of the functionally graded beam with an axial velocity. In this work, the dynamic model of the transverse vibration of the functionally graded beam with an axial velocity is reviewed in brief firstly. Based on the dynamic symmetry breaking theory and the generalized multisymplectic method for the infinitedimensional system, a structurepreserving numerical scheme for the dynamic model is developed. In the numerical simulation, the critical step length satisfying the generalized multisymplectic condition is obtained with the given material parameters. The first six frequencies of the transverse vibration model are presented employing the differential quadrature method, the complex modal method and the structurepreserving method respectively. From the numerical results, it can be found that the first six frequencies obtained by using the structurepreserving method are highly consistent with those obtained by using the complex modal method. To improve the precision of the differential quadrature method, the main factors resulting in the error are investigated. The main contribution of this work is proposing a new approach to analyze the complex dynamic problem like the transverse vibration of the functionally graded beam with an axial velocity considered in this paper.