The tracking problem of free-floating space manipulator system in task space with friction disturbance torque is investigated in this paper. A terminal sliding mode controller is proposed to achieve finite time stabilization of the system. Furthermore, taking into account the existence of dead-zone nonlinearity of the actuator, an adaptive compensator is designed to estimate its upper bound and thus ensure the effectiveness of the proposed controller. Lyapunov stability analysis proves that the closed-loop system is globally asymptotic stable. Numerical simulations show that this controller can effectively achieve inertia space tracking task and also be robust to external disturbances.