To further the technique of indirect measurement, the contact-point response of a moving test vehicle is adopted for the damage detection of bridges. First, the contact-point response of the vehicle moving over the bridge is derived both analytically and in central difference form (for field use). Then, the instantaneous amplitude squared (IAS) of the driving component of the contact-point response is calculated by the Hilbert transform, making use of its narrow-band feature. The IAS peaks serve as the key parameter for damage detection. In the numerical simulation, a damage (crack) is modeled by a hinge-spring unit. The feasibility of the proposed method to detect the location and severity of a damage or multi damages of the bridge is verified. Also, the effects of surface roughness, vehicle speed, measurement noise and random traffic are studied. In the presence of ongoing traffic, the damages of the bridge are identified from the repeated or invariant IAS peaks generated for different traffic flows by the same test vehicle over the bridge.