Membrane has been attracting extensive attention due to their application in various engineering fields. Compared to traditional materials, graphene reinforced composites have demonstrated great potential in developing high-performance and multifunctional membrane structures. It is of great importance to investigate the structural behaviours of such composite membrane with considering damping and their significantly improved dielectric properties. This work studies the damped vibration of graphene nanoplatelets reinforced composite (GNPRC) dielectric membrane. Governing equations are established for the nonlinear damped vibration of the GNPRC dielectric membrane, in which the effects of dielectric properties and damping are incorporated in terms of energy. Taylor series expansion (TSE), differential quadrature (DQ) and direct iterative methods are used to numerically solve the governing equations. The model and the results are validated by comparing present results with previously reported ones. Parametric study is conducted to investigate the effects of the attributes of the electrical field and the GNP fillers, dielectric properties of the composites, damping and the stretching ratio on the nonlinear damped vibration. The result shows that the vibration frequency of the membrane can be actively tuned by changing the attributes of the applied electrical field. When the stretching ratio increases from 1.05 to 1.10, the nonlinear damped frequency can increase by 39.8%, indicating the significant effects of the stretching ratio.