In this paper, the feasibility and sensitivity of damage detection based on dynamic responses of a simply supported beam were examined theoretically and numerically, which were the displacement, velocity and acceleration histories at mid-span on a beam under the moving load. First, the theoretic background of a damage beam vibration subjecting to moving load was briefly described. And then a finite element method was used to calculate the responses of the beam. Using wavelet transform of the dynamic responses, the damage could be identified. Case studies showed that the velocity response was sensitive to the damage and the simulations illustrated the better quality of damage detection by velocity than the ones by displacement and acceleration.