Aiming to overcome the serious disadvantages of two kinds of under-actuated fingers: coupled finger and self-adaptive finger, this paper proposed a novel grasping mode, called Coupled and Self-Adaptive (COSA) grasping mode, which includes 2 stages: firstly coupled and then self-adaptive grasping. A 2-joint COSA finger with double gear-rack-slider mechanisms (called COSA-GRS finger), is developed based on the COSA grasping mode: at the beginning, the 2-joint finger bends with coupled mode, two joints of the finger rotate simultaneously with a fixed ratio until the proximal phalanx touches the grasped object, then the finger will automatically decouple and rotate with self-adaptive mode, the distal phalanx quickly rotates until it touches the object. The new finger unit has the advantages of coupled finger and self-adaptive fingers. The finger is not only able to rotate all joints simultaneously to pre-shape before grasping objects, but also able to self-adapt different sizes and shapes of objects. Using the same mechanism as the 2-joint finger, a 3-joint COSA finger is designed. Force analyses and structure optimization rule of the new finger are given and discussed. The simulation results show that the finger unit is effective: it can successfully realize coupling and decoupling and it can stably grasp objects. An under-actuated humanoid robot hand is developed, called the COSA-GRS Hand. The hand has 5 fingers, 15 joints and 6 motors. All fingers of the hand are COSA fingers. The hand is more similar to human hand in appearance and actions, able to grasp different objects more dexterously and stably than tradition coupled or self-adaptive under-actuated hand.