A cable-suspended camera robot with a large workspace is employed to realize mobile photographs, while the large-span cables with unilateral driving properties introduce many new challenges that need to be addressed, whose structural stability is one of the most critical challenges. As a result, this paper first presents a stability measure method for camera robots while considering the cable mass and sags. Moreover, a stability sensitivity evaluation model for the robot is established with grey relational degree, where the relationship between the stability of the robot and the influencing factors (the cable tensions and the positions of the camera platform) is explored. Finally, the proposed models are supported by doing some simulation studies on a cable-suspended camera robot. The results show that the cable sags of the large-span cables have significant effects on both the cable tensions and the structural stability of the robot, while the stability sensitivity evaluation results indicate the cable tensions have a more important influence on the stability of the camera robot than the positions of the camera platform.