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In this paper, a kind of nonlinear dynamic model of dual-arm free-floating space robot systems is presented based on Lagrange method. Based on the result, the control problem for space manipulator to track the desired trajectory in joint workspace is discussed. Because of the high structure complexity and the parameter uncertainty of space manipulator systems, the scheme of variable structure sliding-mode control with better robustness to uncertainty and disturbance is proposed. Fuzzy controllers are designed at the aim of chattering reduction and rapid response. The fuzzy controllers can tune the sliding control law automatically according to the relationship between system state and switching manifold. The effect of the controller is testified by computer simulation.