The free vibration characteristics of functionally graded thin elliptical cylindrical shells are investigated based on the absolute nodal coordinate formulation (ANCF). Third-order Bézier curve fitting technique is employed to calculate the initial circumferential tangent vector and circumferential arc length of ANCF rectangular shell elements, thereby avoiding the calculation of elliptic integrals and improving fitting accuracy. Starting from the kinetic energy expression and the functional relationship between the Green strain tensor and absolute displacement, the generalized mass matrix, generalized elastic force vector, and generalized stiffness matrix of functionally graded thin elliptical cylindrical shell elements are derived. Using d'Alembert's principle, a system of nonlinear dynamic differential equations is established. At the equilibrium position of the system, a system of linear differential equations of motion for functionally graded thin elliptical cylindrical shells is established by introducing small perturbations to the generalized coordinates. Numerical calculations are performed to analyze the effects of gradient index, elliptical cross-section eccentricity, and length-to-diameter ratio on the natural frequencies of functionally graded thin elliptical cylindrical shells with simply supported ends. The results indicate that the elastic modulus ratio, density ratio, and gradient index of the materials exert a significant influence on the natural frequencies; the natural frequencies of all orders for stainless steel-alumina shells (circumferential wave numbers 1 through 3) decrease with increasing length-to-diameter ratio; the natural frequency corresponding to circumferential wave number 1 increases with increasing eccentricity, and the length-to-diameter ratio is the primary factor influencing the variation of natural frequencies.