A jumping robot has different jumping characteristics. The emphasis of its motion characteristics is placed on the sagittal plane, and every phase of a whole jumping motion has different constraints, so it is a variable constraint system. Its kinematic and dynamic equations, both of the stance phase and of the flight phase are established. Furthermore, the floating basis method is applied to unify the dynamic equations of the stance phase and the flight phase. The generalised coordinate is found based on the union of the tiptoe translation and the joint variables to obtain dynamic equations with constraints. Since the jumping robot is a strongly coupled system and has great impact when it lands on the ground, a reaching law is applied in the development of sliding mode controller in task space such that the state trajectory starting from anywhere can move towards the switching surface, making the system tracking error converge exponentially to zero. Simulation results demonstrate the efficiency and validity of the proposed control system.