Robotic fingers, which are the key parts of robot hand, are divided into two main kinds: dexterous fingers and under-actuated fingers. Although dexterous fingers are agile, they are too expensive. Under-actuated fingers can grasp objects self-adaptively, which makes them easy to control and low cost, on the contrary, under-actuated function makes fingers feel hard to grasp things agilely enough and make many gestures. For the purpose of designing a new finger which can grasp things dexterously, perform many gestures and feel easy to control and maintain, a concept called “gesture-changeable under-actuated” (GCUA) function is put forward. The GCUA function combines the advantages of dexterous fingers and under-actuated fingers: a pre-bending function is embedded into the under-actuated finger. The GCUA finger can not only perform self-adaptive grasping function, but also actively bend the middle joint of the finger. On the basis of the concept, a GCUA finger with 2 joints is designed, which is realized by the coordination of screw-nut transmission mechanism, flexible drawstring constraint and pulley-belt under-actuated mechanism. Principle analyses of its grasping and the design optimization of the GCUA finger are given. An important problem of how to stably grasp an object which is easy to glide is discussed. The force analysis on gliding object in grasping process is introduced in detail. A GCUA finger with 3 joints is developed. Many experiments of grasping different objects by of the finger were carried out. The experimental results show that the GCUA finger can effectively realize functions of pre-bending and self-adaptive grasping, the grasping processes are stable. The GCUA finger excels under-actuated fingers in dexterity and gesture actions and it is easier to control and cheaper than dexterous hands, becomes the third kinds of finger.