The six degrees of freedom (6-DOF) adaptive finite-time control for spacecraft with unknown uncertainties and disturbances approaching to a non-cooperative target is investigated in this study. The system of the spacecraft with coupled relative translation and relative rotation are modeled. Considering the unknown mass and inertia uncertainties and the state-dependent disturbances, a coupled 6-DOF adaptive finite-time tracking control law with a self-adjustment function is developed to achieve high precision proximity operations between chaser and non-cooperative target. The convergence performance is improved by the designed self-adjustment function. The unknown mass, inertia and disturbance are estimated by adaptive update laws. The properties of the proposed control law are discussed through the comparison of simulation results.