This paper presents the influence of the varying axial force of cable-stayed bridge caused by moving vehicles on the detection of diameter reduction of cables using vibration signal obtained from the climbing robot. The cable model is considered as an axially loaded Euler beam. When there is no diameter reduction, the dynamic displacement of the robot is smooth and no distortion can be inspected. When there is a reduction in diameter of the cable, there is a distortion in the robot displacement at the damage location and it can be detected visually. However, when the axial tension force changes as a function of time, this distortion is hidden in the fluctuation of the displacement time history of the robot, thus it is very difficult to be observed visually. Nevertheless, the wavelet transform of the displacement can be applied to detect this hidden distortion. The proposed method is still efficient to detect local changes in diameter with amplitude as small as 1% even when the axial tension force varies as a function of time