Aiming at the large-angle maneuver control problem of tracking spacecraft attitude in non-cooperative target rendezvous and proximity tasks, under the condition that the target spacecraft attitude information is unknown and the actuator output has physical limitations, a limited-time autonomous control method is proposed. First, an end-to-end pose estimation network is designed based on adaptive dual-channel feature extraction and dual attention. The information around the target is obtained through the adaptive dual-channel feature extraction module. The addition of spatial attention and channel attention allows the network to learn the target’s characteristics more accurately. Secondly, based on the improved adaptive update law, a finite-time saturation controller is designed using the hyperbolic tangent function and the auxiliary system. The hyperbolic tangent function can strictly ensure that the control torque of the control system is bounded. Finally, the simulation results show that the proposed autonomous control method can accurately estimate the attitude of the non-cooperative target spacecraft and can maneuver to the target attitude within 20 s under the condition that the actuator’s output is physically limited.