This study investigates the vibration response of a functionally graded beam subjected to a two-degree-of-freedom moving load using the finite element method. The finite element formulations for the dynamic analysis of the classical functionally graded beam are derived based on Hamilton’s variational principle. A MATLAB program is developed to compute the vibration response employing the Wilson–θ numerical integration algorithm. In addition, a semi-analytical solution is established to validate the finite element results proposed in this study. The comparison results demonstrate excellent agreement between the finite element method and the semi-analytical approach in predicting the beam’s vibration response. Parametric studies with various input conditions clearly reveal the significant influence of the load magnitude and load velocity on the dynamic behavior of the system. Furthermore, the results indicate that the dynamic amplification factor increases markedly with increasing velocity. Unlike previous FEM studies using simplified moving loads, this work explicitly formulates the coupled mass, damping, and stiffness matrices including Coriolis and centrifugal effects for a 2-DOF vehicle–FGM beam system. Unlike previous FEM studies using simplified moving loads, this work explicitly formulates the coupled mass, damping, and stiffness matrices including Coriolis and centrifugal effects for a 2-DOF vehicle–FGM beam system.