A negative pressure wall-climbing robot is a special robot for climbing vertical walls, which is widely used in construction, petrochemicals, nuclear energy, shipbuilding, and other industries. The mobility and adhesion of the wheel-track wall-climbing robot with steering-straight mode are significantly decreased on the cylindrical wall, especially during steering. The reason is that the suction chamber may separate from the wall and the required driving force for movement increases, during steering. In this paper, a negative pressure wall-climbing robot with omnidirectional movement mode is developed. By introducing a compliant adjusting suction mechanism and omni-belt wheels, an omnidirectional movement mode is formed instead of the steering-straight mode, and the performances of adhesion and mobility are improved. We establish the safety adhesion model for the robot on a cylindrical wall and obtain the safety adhesion forces. We designed and manufactured an experimental prototype based on the analysis. Experiments showed that the robot has the ability of full maneuverability in cylindrical walls.