In the present work, the nonlinear free flexural vibration of thick curvilinear fiber composite laminates is investigated using a higher-order shear flexible eight-noded quadrilateral element developed considering the variation of in-plane and transverse displacement through the thickness. The formulation includes both the geometric nonlinearity and inertia effects. The governing equations, derived based on Lagrange’s equations of motion, are solved iteratively through an eigenvalue approach. The formulation is tested against various problems for which the solutions are available in the literature. A detailed analysis is made to assess the influence of fiber angles, lamination schemes, boundary conditions, thickness, and aspect ratios on the nonlinear frequency ratio at large amplitude vibrations of the laminates. A comparative study is also done along with the first-order and simple higher-order theory deduced from the present model by neglecting the thickness stretching effects. The present analysis shows the degree of hardening behavior getting affected noticeably compared to those of the traditional straight fibers, thus exhibiting the occurrence of drop off in frequency ratio and redistribution of mode shapes at certain amplitudes of vibration.