Abstract: Based on a new type of the high-order beam theory, this paper studies the free vibration of beams of functionally graded materials (FGM). The finite element method is used for the new high-order beam theory. The discrete dynamic balance equation is derived by using the Hamilton principle, and the C1 type high-order beam element with 2 nodes and 8 degrees of freedom is constructed. The modal analysis of the homogeneous cantilever beam is carried out, and the accuracy of the beam element is verified. Then the modal analysis of the FGM beam is carried out by using the element, and a dimensionless natural frequency with a weak material correlation is formulated. Based on the dimensionless natural frequency, the transformation relationship between the natural frequency of the beam of the functionally graded materials and that of the homogeneous beam is established. The applicable conditions of the transformation relationship are analyzed by numerical simulations.