In this paper, the dynamic response of functionally graded nanocomposite beams under the action of a moving load are investigated. Three different types of Carbon NanoTubes (CNT’s) distributions in a polymer matrix material are studied; Uniform Distribution (UD), Symmetrically Functionally Graded (SFG) distribution and Unsymmetrically Functionally Graded (USFG) distribution. The analysis is carried out by a mesh-free method using the two-dimensional theory of elasticity. After validation, the effects of different design parameters such as CNT’s distribution, the velocity and position of the moving load on the dynamic behavior of the beam are examined. The results also highlight the importance of the reinforcement distribution type from a design perspective. The current approach can serve as a benchmark against which other semi-analytical and numerical methods based on classical beam theories can be compared.