Robotic systems are expected to play an increasingly important role in future space activities with the development of space technology. The robotic on-orbital service, whose key is the capturing technology, becomes research hot in recent years. This paper focuses on the guidance of a robot manipulator to capture a spinning satellite with unknown dynamics parameters. In capturing a spinning satellite, a reference trajectory for control of the manipulator is generated with time delay due to the processing time of the target motion estimator and the manipulator controller. Consequently, the control system shows a poor performance and the end-effector sometimes fails to capture the target satellite. To solve this problem, the motion characteristics and motion prediction of the spinning satellite is analyzed Firstly, and using Unscented Kalman Filter (UKF) to predict its movement. Then, a method of autonomous path planning of a free-floating space robot for target capturing is proposed, which is based on motion prediction and speed compensation. Finally, a ground experiment system is set up based on the concept of dynamic emulation and kinematic equivalence. With the experiment system, the autonomous target capturing experiments are conducted. The experiment results validate the proposed algorithm.