Continuous trajectory tracking control in task space of free-floating space robots was investigated. An adaptive RBF based terminal sliding mode control method was proposed for a dynamics model with unknown nonlinear terms, parametric uncertainties and unbounded external disturbances. The proposed method combines the properties of a nonlinear sliding manifold with that of a radial basis function, where the adaptive RBF network is used to estimate the unknown parts of the system on line, such that rapid convergence of control errors in finite time are guaranteed without the exact dynamics mode of the system. The adaptive updating laws were designed according to Lyapunov approach, which make the closed-loop control system globally stable and eliminate chattering problems. A six-link free-floating space robot was employed to validate the proposed method. The simulation results show that the adaptive RBF based terminal sliding mode control method provides high precision performances without the exact dynamics model. Meanwhile, the chattering problems were eliminated effectively.