The radial point interpolation method (RPIM) is proposed for dynamic analysis of a rotating functionally graded rectangular plate. Considering the non-linear coupling deformation which means the in-plane longitudinal shortening terms caused by transverse deformation, the dynamic equations is established via employing Lagrange’s equations of the second kind. The simulation results of first-order approximation coupled (FOAC) dynamic model are compared with those of traditional zero-order approximation coupled (ZOAC) dynamic model, which shows the results using FOAC are more accurate, especially in the situation of high rotating speed. Meanwhile, the effect of the functionally graded index on the dynamic characteristics is discussed. The results show that the lateral deformation of the rotating plate increase with the functionally graded index increasing. In addition, the simulation results are compared with finite element method and assumed mode methods, which shows the superiority of RPIM.