Abstract: The rigid-flexible-thermal coupling dynamics of a rotating internal FGM (functional gradient materials) beam system is studied. The beam is assumed to be of a Euler–Bernoulli type, made of two-component materials, and its mechanical properties change in a power law along the thickness direction. The transverse bending deformation and axial tensile deformation of the flexible beam are considered, and the longitudinal shortening caused by the transverse bending, namely the nonlinear coupling term, is taken into account. The deformation field of the flexible beam is discretized by the assumed mode method, and the first-order approximate rigid-flexible-thermal coupling dynamic equation of the system is derived by using the second kind of Lagrange equation, and the dynamic simulation software of the rotating internal FGM beam is compiled. Then the effects of various dimensionless parameters and temperature changes on the natural frequency, critical speed and dynamic characteristics of the system are studied in detail. The results show that the hub radius ratio, functional gradient coefficient and temperature change of the internal FGM beam have great influence on the dynamic characteristics of the system.