In this paper, a numerical algorithm using a coupled finite element-differential quadrature (DQ) method is proposed for the dynamic analysis of laminated composite coated beams subjected to a stream of accelerating oscillators. The finite element method with cubic Hermitian interpolation functions is used to discretize the spatial domain. The DQ method is then employed to discretize the time domain. The resulting set of algebraic equations can be solved by either direct methods or iterative methods. It is revealed that the DQ method stands out in numerical accuracy, as well as in computational efficiency, over the well-known standard finite difference schemes, such as the Newmark, Wilson $\theta $, Houbolt, and central difference methods, for the cases considered. Furthermore, in the numerical examples, the effects of various parameters having something to do with the title problem, such as lamina thickness, orientation of the coats, arrival time intervals, velocities, and accelerations of the oscillators on the dynamic behavior of the system, are investigated. The technique presented in this investigation is general and can be easily applied to any time-dependent problem.