Reaction null space (RNS) planning and control of a planar three-link space manipulator’s pregrasping a spinning target are studied. First, the Lagrange dynamic model of the manipulator was established. Second, the RNS motion planning algorithm was derived, and the vector norm constraint algorithm of RNS planning was addressed to ensure certain joint angular acceleration constraints were satisfied. Furthermore, an augmented adaptive sliding mode controller based on time delay estimation (TDE) was proposed. This controller estimated the unknowns of the system by TDE technology, in which accurate and complete dynamics were not required, and an adaptive TDE was introduced to decrease the estimation errors and avoid serious chattering. Finally, numerical simulations were carried out to verify the effectiveness of the proposed RNS planning and control algorithm.