The present study probes the nonlinear free vibrations of viscoelastic polymeric composite plate reinforced by carbon nanotubes. For this purpose, Kelvin-Voigt model is utilized. Moreover, the equations of motion are extracted by the Hamilton principle and taking into account Von Karman nonlinearity. In order to solve and analyze nonlinear free vibrations, the researchers utilized multiple scales method. Thanks to this method, the normal nonlinear frequencies of the system were obtained, and as well, the impact of various factors such as dampness coefficient, material viscosity and carbon nanotubes volume fraction were investigated. Besides, the thickness-dimension ratio of the plate and its impact on the normal frequency was also studied. The findings of the study highlighted that an increase in the ratio of plate’s thickness to its length causes an increase in the normal nonlinear frequency of the plate. Additionally, as the volume fraction of the carbon nanotubes increases, system’s normal nonlinear frequency increases as well. Finally, the impact of different distribution of carbon nanotubes on the normal nonlinear frequency and system’s time response was also probed. As it could be vividly observed, nonlinear frequency for FGO distribution was reported to be further than uniform distribution, but the trend was in reverse for FGX distribution.