In this paper, we present a bioinspired design for a cat-paw-inspired tree-climbing robot gripper using a combination of soft and hard design. We draw lessons from the cat's tree-climbing action and the structural function of the cat's paw and extract and focus on the key features: the structure of the paw's skeleton, the unique structure of the end claw provides the grip ability, and the stability and friction provided by the soft tissues of the meat pad. In view of the excellent tree-climbing ability of cats, the cat-paw robot gripper in this paper is different from the traditional tree-climbing robot, which is suitable for the complex tree environment. This is also an inspiration for the paw design of the quadruped robot to complete the climbing action. In this paper, the design mainly focuses on the analysis of principle, mechanical structural design, simple motion demonstration and general control system.