This article presents a 6-DOF attitude-orbit synchronous control problem for the space circumnavigation (SCN) mission with parameter uncertainties, time-varying uncertainties, and input constraints. In particular, from the perspective of engineering application, time-varying measurement uncertainties are taken into account of the 6-DOF attitude–orbit coupling kinematics and dynamics, and the analytical solution of the desired attitude is derived based on the measured relative orbit information with measurement uncertainties. To drive the active spacecraft approach to the faulty target safely, a time-varying exponential prescribed convergence boundary is introduced into the sliding surface. A finite-time disturbance observer is involved in equivalent tracking errors for compensating the mismatched uncertainties. In addition, an auxiliary system is designed to overcome the instability danger caused by input constraints. The stability of the controlled system is discussed in the nonautonomous finite-time stable framework, which is proved via Lyapunov analysis that the attitude-orbit tracking errors converge to the equilibrium within finite time. The simulation experiment with mismatched uncertainties and prescribed constraints shows the superiority of the designed control scheme.