In some existing omnidirectional mobile robots, the movement of each wheel is generally controlled by one driven motor cooperates with one steering motor, such design will increase the energy consumption. This paper investigates an omnidirectional mobile robot based on a special coupling system, so as to solve the above problem. We propose a unique robots steering method by designing the parallelogram connecting rod as the coupling system, which makes each wheel only need to be equipped with one motor to complete omnidirectional motion and always keep unchanged robots attitude. In theory, we conduct the structural analysis, dynamic analysis and kinematic analysis of the mobile robot and explain why our system is under-actuated. In experiments, the square trajectory and the serpentine trajectory are exploited to verify the rationality of design and theoretical derivation by comparing the simulation results with the experimental results. By performing mobile robot walking experiments under different ground condition respectively, the stability and adaption of the under-actuated omnidirectional mobile robot is also favourably confirmed. After detailed theoretical analysis and the support of experiments, it is carried out that the under-actuated mechanism proposed in this paper can indeed realize the movement of the robot in all directions. As well as the attitude of the robot always keeps constant, as we expected, enables to realize the steering of robot flexibly even in a narrow space.