The geometric nonlinearity-based free vibration analysis of shear deformable functionally graded material (FGM) plates is investigated in this paper. The nonlinear finite element equations are derived from hybrid hyperbolic higher-order shear deformation theory (HSDT). The Green–Lagrange nonlinear strain–displacement relation is incorporated in the formulation, along with all higher-order nonlinear strain terms to account for the geometric non-linearity developed during analysis. Typically, the constituent isotropic ceramic and metal phases follow a simple power-law distribution with the composition varying gradually with plate thickness. By adopting traction-free boundary conditions on the top and bottom faces of the plate, the fundamental equations are derived using a variational approach. An efficient C0 continuity finite element formulation with 7 degrees of freedom (DOFs) per node is developed using homemade MATLAB code to produce the fundamental frequency and mode shape results. To prove the efficacy of the current model, convergence tests are conducted and the results are validated with existing literature. Parametric studies are performed for varied thickness ratios, aspect ratios, skewness of the plate, and volume fraction index with different boundary conditions, the fluctuation of nonlinear frequency ratio with amplitude ratio is highlighted.