In the present study, linear dynamic analysis of an axially functionally graded (AFG) beam with simply-supported edges due to a moving harmonic load has been analyzed by using Euler-Bernoulli beam theory. Elasticity modulus and mass density of the beam vary continuously in the axial direction of the beam according to a power-law form. The equation of motion is derived by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG beam is expressed in modal form, and Newmark method is employed to find the dynamic responses of AFG beam. In this study, the influences of material distribution, velocity of the moving load and excitation frequency on the dynamic response of the beam are investigated. In order to establish the accuracy of the present formulation and results, the first three free vibration frequencies are obtained, and compared with the published results available in the literature. Good agreement is observed. Results indicate that the above-mentioned effects play a very important role on the dynamic responses of the beam, and it is believed that new results are presented for non-linear dynamics of FG beams under moving loads which are of interest to the scientific and engineering community in the area of FGM structures. (c) 2012 Elsevier Ltd. All rights reserved.