A temperature-dependent vibration analysis is conducted for the functionally graded nanocomposite beams which are reinforced by graphene. Material properties are assumed to change along the beams in five different types based upon the graphene distribution with a specific function. The differential equations of motion are extracted and solved using the spectral numerical method for the beams under various boundary conditions. The effect of distribution of functionally graded nanocomposite in the thickness direction of beams on the frequency response of vibration, and the effect of various parameters on the vibration response has been examined, such as the distribution function of nanographene plates, weight percentage, dimensions of nanographene plates, temperature changes, and thickness ratio. The results are compared and validated with numerical and analytical results reported in references for manifold boundary conditions. It is seen that the increase of graphene weight percentage in all boundary conditions will cause an increase in the natural frequency of the beams.