Space robots play a more and more important role in on-orbit service missions. It is essential for a space robot to stabilize its attitude rapidly after capturing an unknown target, because of its residual momentum. Regarding uncertainties in inertial parameters of the target, process and measurement, and insufficient measurements, this paper first presents extended Kalman filter (EKF) enhanced model predictive control (MPC) strategy for rapid attitude stabilization of space robots with bounded control torque of the actuator and the manipulator in postcapture, in which motion of the manipulator is planned to make up for the limitation of the actuator. Thanks to the Jacobian matrix, which is required for EKF, the linear varying time-MPC is applied to handle the constraints of the drive torque, which can be solved by the online active set method effectively and efficiently. Simulation has been done for the 2D and the 3D models, and the results show that the whole system, including the base and the manipulator can be stabilized, and inertial parameters of the target can converge to their ideal values with the constraints. In addition, robustness of the presented method has been verified by Monte Carlo simulation.