Capture is a key component for on-orbit service and space debris clean. The current research of capture on-orbit focuses on using special capture devices or full-actuated space arms to capture cooperative targets. However, the structures of current capture devices are complex, and both space debris and abandoned spacecraft are noncooperative targets. To capture non-cooperative targets in space, a lightweight, less driven under-actuated robotic hand is proposed in this paper, which composed by tendon-pulley transmission and double-stage mechanisms, and always driven by only one motor in process of closing finger. Because of the expandability, general grasping model is constructed. The equivalent joint driving forces and general grasping force are analyzed based on the model and the principle of virtual work. Which reveal the relationship among tendon driving force, joint driving forces and grasping force. In order to configure the number of knuckles of finger, a new analysis method which takes the maximum grasping space into account, is proposed. Supposing the maximum grasped object is an envelope circle with diameter of 2.5 m. In the condition, a finger grasping maximum envelope circle with different knuckles is modeled. And the finger lengths with corresponding knuckles are calculated out. The finger length which consists of three knuckles is the shortest among under-actuated fingers consists of not more than five knuckles. Finally, the principle prototype and prototype robotic hand which consists of two dingers are designed and assembled. Experiments indicate that the under-actuated robotic hand can satisfy the grasp requirements. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.