This paper proposes two items: One is a sliding mode based on a new concept concerned with redundancy. The other is a control scheme based on that concept for a redundant manipulator in space to grasp a floating object. The previously published methods required many calculations becasuse of using pseudo inverse. To deal with this problem, we introduce a new concept of redundancy based on redundancy of sliding mode itself, and introduce a new sliding mode. This concept is combined with a conventional sliding mode control method. By using this hybrid control scheme the number of calculations is reduced to about 1/5 or 1/6 for tracking the same trajectory of an end-effector utilizing the redundancy as that of the conventional methods. And the proposed control method eliminates the necessity of the estimation of uncertain motion parameters of translational and rotational momenta by adaptive gains. Finally the effectiveness of the proposed method is verified by computer simulations for the trajectry control where the satellite angular velocity is surpressed by taking advantage of redundancy based on a new concept.