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In this paper, the control problem of free-floating dual-arm space robot system with uncertain parameters is studied. Because the base of dual-arm space robot is not controlled and it is free-floating, the dynamic equations of space robot system no longer are linearly parameterized. It results the control of space robot system becomes very difficult. Based on the idea of augmentation approach, the difficulty proposed above is overcome, and the robust adaptive composite control scheme for dual-arm space robot to track the desired trajectory in inertial space is developed. The asymptotic stability of the control scheme is proved with Lyapunov method. A planar free-floating dual-arm space robot system with two payloads is simulated to verify the proposed control scheme.