This paper discusses the motion control problem of kinematically redundant hybrid parallel robots that were recently proposed. The kinematic and dynamic models are firstly reviewed. It is pointed out that the robot can be decomposed into two parts and that each part can be analysed independently. A new hybrid approach is proposed based on this property of the robot. This approach includes an adapted computed-torque control scheme for the legs that operates in the joint space as well as a compensation of the errors of the platform applied in the Cartesian space. The convergence of this proposed approach is also verified using the Lyapunov stability theory. Two example architectures of kinematically redundant robots are built and experiments are conducted. Finally, the results are compared and analysed in order to validate the improvements provided by the proposed control method. It is shown that the proposed control scheme significantly reduces the position error. Potential extensions of this work are also discussed.