This paper discussed control problem of dual-arms space-based robot system with unknown payload parameters to track desired trajectory in joint space, when the attitude of base was controlled and its location was uncontrolled. Combining the relationship of the linear momentum conversation and the Lagrange approach, the full-controlled dynamic equation of space-based robot system with dual-arms were analysed and established. Based on the above results, for the case of dual-arms space-based robot system with unknown payload parameters, a composite control scheme was designed by a computed torque controller and a fuzzy compensator to track desired trajectories in joint space, i.e., balancing the effect of system unknown payload parameters on computed torque controller with fuzzy adaptive compensator, in order to ensure the whole closed-loop control system asymptotic stability with the existence of unknown payload parameters. The mentioned control scheme can effectively overcome the effect of system unknown payload parameters and control both the base attitude and the joints of dual-arms space-based robot, so that they can track the desired trajectory in joint space, with obvious advantages neither the mentioned control scheme needs to measure and feedback the position, velocity and acceleration of the floating base, nor the mentioned control scheme needs to require for dynamic equations of the system inertial parameters in linear function. The simulation results show that the proposed control scheme is feasible and effective.