This paper develops a geometrically nonlinear coupled finite element model for high-speed rotating AFG beams using the complete Green–Lagrange strain tensor. The model extends the complete Green–Lagrange formulation, previously used for homogeneous rotating beams, to AFG beams and retains all higher-order axial nonlinear terms. Instead of directly adding a density-dependent centrifugal stiffening term, it solves the steady-state axial deformation from dynamic equilibrium and uses it as an intermediate variable carrying the joint distribution of $E\left(x\right)$ and $\rho \left(x\right)$, so that both properties enter the geometric stiffening terms. The gyroscopic coupling matrix $\mathbf{G}$ is fully retained. Numerical results show that (i) under the present Green–Lagrange formulation, the model predicts a monotonic stiffening trend consistent with complete stiffening in the limiting case at high rotational speeds, whereas the conventional centrifugal-force model can exhibit nonphysical softening under the fully coupled formulation; (ii) the coupled model captures frequency veering and mode exchange; and (iii) the steady-state tip deformation and first bending frequency show opposite trends with k. These results provide a reference for gradient design of rotating AFG beams within the considered parameter range.