For the large redundant manipulator, due to its long working distance and large mass, the number of links (i.e., manipulator’s arms) that can be driven to move simultaneously is limited. Otherwise, the control accuracy and motion stability of the manipulator will deteriorate. Focusing on that, a weighted Newton iteration (WNI) algorithm for trajectory planning of the manipulator is firstly proposed, where the motion of the manipulator joints is controlled by a weight matrix, which is constant and related to each link’s energy consumption. To dynamically adjust the weight matrix according to kinematic constraints and acquire better energy efficiency, an adaptive WNI (AWNI) algorithm is further proposed. In AWNI, the weight matrix is adjusted in real-time during the planning process, with considerations of the kinematic constraints and the energy consumption of the manipulator. The switch of the links between the working state and the non-working state is made through the weight matrix to achieve flexible control of the manipulator motion. Two evaluation functions are established to validate the effectiveness of AWNI in energy saving and motion stability control. Taking a 6 degrees of freedom (DOF) manipulator as an example, simulation experiments on trajectory planning are carried out and the results show the effectiveness of the proposed AWNI algorithm.