The nonlinear vibration of carbon nanotube-reinforced beam (CNTRC) subject to a nonlinear Winkler-Pasternak foundation and a mechanical impact is analyzed in this work. Considering a straight CNTRC beam made of a mixture of single-walled carbon nanotubes and an isotropic polymer matrix. A higher-order shear-deformation beam theory is applied for Reddy beam. The governing equations are established based on the von Karman theory and Hamilton’s principle. The obtained nonlinear system is discretized by means of Galerkin-Bubnov procedure and according to this model the corresponding nonlinear ordinary differential equations are solved by means of a proper procedure, namely the Optimal Homotopy Asymptotic Method (OHAM), which introduce the so-called auxiliary functions and some convergence-control parameters which are optimally determined so that the approximate analytical solution to be nearly identical with numerical integration results obtained by means of a classical Runge-Kutta method.