The　volume　fraction　of　the　carbon　nanotube　(CNT)　plays　a　key　role　in　ensuring　the　performance　of　the　CNT　reinforced　polymer　composite,　especially　under　the　severe　vibration,　which　leads　to　the　resonance　and　failure　of　the　composite　structure.　In　this　paper,　a　bottom-up　multiscale　method　is　adopted　to　study　the　effect　of　the　CNT　volume　fractions　on　the　nonlinear　vibration　of　the　poly　(methyl　methacrylate)　(PMMA)/CNT　composite.　According　to　the　molecular　simulation,　the　longitudinal,　transverse　and　shear　moduli　of　the　PMMA/CNT　nanocomposites　are　found　to　increase　with　the　increasing　CNT　volume　fractions.　Substituting　the　simulated　moduli　into　the　extended　rule　of　mixtures　(EROM),　the　efficiency　parameters　of　the　PMMA/CNT　composite　with　various　CNT　volume　fractions　are　derived　based　on　a　homogenization　approach.　The　derived　efficiency　parameters　are　used　in　the　functionally　graded　(FG)-based　EROM　to　obtain　the　expressions　of　the　longitudinal,　transverse　and　shear　moduli　of　the　macroscopic　composite　plate,　so　as　to　obtain　the　constitutive　equation　for　the　nonlinear　vibrations　of　the　FG-based　PMMA/CNT　composite　plate.　The　subsequent　meshless　simulation　results　demonstrate　that　the　natural　frequencies　of　the　FG-based　composite　plate　increase　with　the　increasing　volume　fractions,　whereas　the　ratios　of　the　nonlinear　to　linear　frequencies　decrease.　Using　the　bottom-up　multiscale　analysis,　the　macroscopic　vibration　responses　are　analyzed　for　the　PMMA/CNT　composites　with　the　CNT　volume　fractions　up　to　9.0%,　which　provides　a　paradigm　of　the　design　of　the　PMMA/CNT　composite　by　considering　the　CNT　volume　fraction　effect.