As important auxiliary equipment, rehabilitation robots are widely used in rehabilitation treatment and daily life assistance. The rehabilitation robot proposed in this paper is mainly composed of an omnidirectional mobile platform module, a lower limb exoskeleton module, and a support module. According to the characteristics of the robot’s omnidirectional mobility and good stiffness, the overall kinematic model of the robot is established using the analytical method. Passive and active training control strategies for an omnidirectional mobile lower limb exoskeleton robot are proposed. The passive training mode facilitates the realization of the goal of walking guidance and assistance to the human lower limb. The active training mode can realize the cooperative movement between the robot and the human through the admittance controller and the tension sensor and enhance the active participation of the patient. In the simulation experiment, a set of optimal admittance parameters was obtained, and the parameters were substituted into the controller for the prototype experiment. The experimental results show that the admittance-controlled rehabilitation robot can perceive the patient’s motion intention and realize the two walking training modes. In summary, the passive and active training control strategies based on admittance control proposed in this paper achieve the expected purpose and effectively improve the patient’s active rehabilitation willingness and rehabilitation effect.