Abstract: The control problem of coordinated motion of a free-floating dual-arm space robot with external disturbance is discussed. Combined the relationship of the linear momentum conversation and Lagrangian approach, the full-controlled dynamic equation of a free-floating space robot with dual-arms is established and then inverted to the state equation for control design. Based on the above results and the terminal sliding mode control (SMC) technique, a mathematical expression of the terminal sliding surface is proposed, and then the terminal SMC scheme of coordinated motion between the base’s attitude and the end-effectors of the free-floating dual-arm space robot with external disturbance is developed. This proposed control scheme not only guarantees the existence of the sliding phase of the closed-loop system, but also ensures the convergence of the output tracking error in a finite time period. In addition, because the initial state of the system is always at the terminal sliding surface, the control scheme can eliminate the reaching phase of SMC and guarantee the global robustness and stability of the closed-loop system. A planar free-floating space robot with dual-arms is simulated to verify the feasibility of the proposed control scheme.