In this paper, we propose a robust control scheme for a free-floating space robot system where a robot arm is mounted on a free-floating base-a satellite, spacecraft or space station. The base is not controlled by external moments or forces. We model the system as an extended robot, including a pseudo-arm representing the base motion produced by six hypothetical passive joints, and a real robot arm. This model allows us to categorize the free-floating space robot system as a specific type of under-actuated system with mixed passive and active joints. We then discuss some fundamental properties of such a system. By means of an input-output linearization technique, we demonstrate that the internal dynamics of the system are nonlinear parametric and therefore, the control of the system using conventional robot control schemes is not feasible. To overcome the difficulty in controlling the internal dynamics subject to parameter uncertainty, and to avoid the measurement of the base acceleration, we develop a robust control scheme based on the second method of Lyapunov. We illustrate an example of a six-degrees-of-freedom space robot system to show the computational procedure and simulation results.