Abstarct: In this rsearch, nonlinear vibration of a functionally graded viscoelastic beam under the action of a moving load have been studied. First, the governing equation of linear vibration of a FGV beam, baxsed on Euler-bernoulli beam theory and Kelvin-voigt viscoelastic model, using Hamilton principle is derived. Natural frequencies and damping factors of a simply supportd beam have been obtained using the method of varaiable separation and the approximate method of Galerkin. By comparing them with the previous references, very good overlap between results have been observed. Then the general solution to the free vibration and particular solution to the forced vibration have been obtained. Also the free vibration when the force leaves the beam have been obtained and the effects of functionally graded parameters on the first natural frequency and damping factor have been investigated. In the next section, the nonlinear equation of motion considering Von-Karman strain relation and Euler-bernoulli beam theory using Hamilton principle is derived. Nonlinear free vibration of beam using multiple-scales have been analyzed and nonlinear natural frequency and the solution of nonlinear free vibration is obtained and variation of the amplitude of the first vibration mode and vibration of beam versus time have been investigated. In the lasr section the forced nonlinear vibration, primary resonance and steady state solution using the method of multiple-scales have been analyzed and the effects of the amplitude of excitation and functionally graded parameters on the frequency response have been studied.