Cable is the most important bearing structure of the cable-stayed bridges. Its safety has been of crucial public concern. Traditional manual cable inspection method has many defects such as low inspection efficiency, poor reliability and hazardous working environment. In this paper, a new wirelessly controlled cable-climbing robot enabling safe and convenient inspection of stay cables is proposed. The designed robot is composed of two modules, joined by four turnbuckles to form a closed structure that clasps the cable. The robot is controlled wirelessly by a ground-based station, and a DC power is supplied via an onboard lithium battery. The climbing principle and mechanical structure of this robot are introduced. The static model of the robot during obstacle negotiation is established. The relationships of the driving force and resistance with obstacle height to determine the obstacle-negotiation capability of the robot are obtained. The effects of cable diameter, cable inclination and preload force on obstacle climbing ability of the robot are also analyzed. The experiments verify that the robot could climb random inclined cables and overcome an obstacle of 2.42 mm in height with a mass of 5 kg payload.