Abstract: The integral expression of dynamic deflection of the beam on viscoelastic foundation to a load moving with variable speed is derived using modal superposition and Duhamel's integral. By employing Gauss-Legendre integration rule, a practical example is chosen to obtain the numerical results. The influences of initial moving velocity, acceleration and parameters of subgrade on the dynamic deflection are discussed. The results indicate that the initial velocity of the moving load have influence on the dynamic response. The dynamic deflection of beam decreases significantly with the increase of the initial moving velocity and acceleration. In addition, it is found that the dynamic deflection of beam decreases with the increase of the shear coefficient, damping and elastic foundation modulus of the foundation and the hysteresis of the dynamic response of the beam is related to the damping, as the damping goes higher, the hysteresis becomes more obvious.