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Compared with the traditional mobile robots, the new concept mobile robots have greater deformation capability and richer mobile gait; similarly, they have a better capability to adapt to the environment. This paper presents a ring four-array rolling mechanism that consists of four anti-parallelogram mechanisms with revolute joints. The mechanism is connected by four anti-parallelograms in a looped configuration and has a not-totally-closed ring shape, whose external contour is similar to that of a quadrangular prism. The mechanism has planar and spherical patterns of locomotion, in which the planar pattern of locomotion includes the parallelogram rolling gait and the anti-parallelogram tumbling gait, and the spherical pattern of locomotion includes the spherical rolling gait. On this basis, the kinematic analysis of the two patterns of locomotion is carried out to obtain the positions of each point and the center of mass (CM) of the mechanism. The feasibility of the rolling locomotion of the mechanism is verified by the moving trajectory of the CM. According to analyzing the feasibility of the mechanism's obstacle-crossing and moving strategy, the mechanism is made to complete the switch between different motion modes. Through the establishment of a dynamic model and simulation, the analysis of the rolling gait of the mechanism is completed, and a prototype is made for experimental research. The results show that the anti-parallelogram ring four-array rolling mechanism has the basic rolling capability of linear movement and steering. Furthermore, in the initial state of the mechanism, the mechanism enables flexible switching between multiple rolling gaits.