The vibration behavior was investigated of thin-to-moderately thick functionally graded carbon nanotube (FG-CNT) reinforced composite quadrilateral plates resting on elastic foundations. In the study, transverse shear and rotatory inertia were incorporated through first-order shear deformation theory. The improved moving least-squares-Ritz method was employed to derive the eigenvalue equation of the plate vibration. The study examined the effects of the elastic Winkler medium, CNT ratios, distributions of CNTs, boundary conditions, side angles, thickness-to-width ratios, and the relative plate aspect ratios on the vibration response of the FG-CNT reinforced composite plates. A set of vibration frequencies and mode shapes for the FG-CNT reinforced composite quadrilateral plates is presented. Additionally, a comprehensive parametric study and vivid mode shape plots demonstrate details of the vibration spectrum of the FG-CNT reinforced composite plates.