The capture of a tumbling free-floating object in orbit using an autonomous vehicle is a key technology for many future orbital missions. Spacecraft proximity operations will play an important role in the success of such missions. This paper technically presents a control approach for proximity operations between a target and a pursuer spacecraft that ensures accurate relative position tracking as well as attitude synchronization. Specifically, an integrated six degrees of freedom dynamics model is first established to describe the coupled relative motion of the pursuer with respect to the target. Then, a robust fault-tolerant tracking control scheme is proposed by combining the sliding mode control with the adaptive technique. It is proved that the control algorithm developed is not only robust against unexpected disturbances and adaptive to unknown and uncertain mass/inertia properties of the pursuer, but also able to accommodate a large class of actuator faults. In particular, by introducing a novel timevarying forcing function into the sliding dynamics, the designed controller is shown to guarantee the finite-time convergence of the translational and rotational tracking errors, and the convergence time as an explicit parameter can be assigned a priori by the designer. Furthermore, a rigorous theoretical analysis is also presented in order to assess the fault-tolerance ability of the designed controller. Finally, numerous examples are carried out to evaluate the effectiveness and demonstrate the benefits of the overall control approach.