Abstract: This paper discusses the design of an improved nonlinear disturbance observer (NDO), a novel adaptive dynamic terminal sliding mode control, and the elastic vibration suppression problem of the dual-arm elastic-joint space robot. Firstly, assuming that the joint of the space robot is elastic, an elastic joint space robot model is established based on the structure of the nonlinear cascade system. The model can be divided into an outer loop manipulator dynamic model and an inner loop joint dynamic model with asymptotic stability. Then, for the dynamic model of the outer loop manipulator, a novel adaptive dynamic terminal sliding mode control algorithm is designed based on the improved NDO. For the inner loop joint dynamic model, the torque feedback control algorithm is designed to suppress the elastic vibration of the flexible joints. The adaptive dynamic terminal sliding mode control algorithm is designed based on the nonlinear cascading system proposed in this paper with good dynamic characteristics and robustness. It can quickly suppress the vibration of the elastic joints under the condition of small flexible stiffness of joints, and achieve the accurate trajectory tracking of the space robots. The system simulation comparison test shows the effectiveness of the control algorithm.