The end of traditional robot fingers moves along a circular trajectory in parallel grasping mode, and it isn't suitable for grasping thin plates on working platform due to its small workspace. For this problem, a co-circular slider straight-line mechanism is proposed, and its working principle, kinematics, and workspace are analyzed. Based on the proposed straight-line mechanism, a novel linear-parallel and self-adaptive robot hand is designed. The proposed robot hand consisting of 2 fingers with 4 degree of freedom (DOF) in total, is driven by only 2 motors, which makes the structure of the hand much simpler. Each finger includes a base, a motor, a spring, an L-shaped linkage, 2 phalanxes, and so on. The proposed device can execute linear-parallel pinching grasping mode and self-adaptive grasping mode, and it has high pinching accuracy and can deal with objects with different positions, shapes, and sizes without additional sensing and control systems. Different grasping modes, kinematics and forces of the designed robot hand are analyzed, and the influence of different parameters on grasping force is studied, which lay a basis for the design and optimization of the robot hand. Besides, a prototype of the proposed hand is developed, with which grasping experiments are conducted. The experimental results indicate that the design and analysis of the robot hand are reasonable, the device can achieve linear-parallel and self-adaptive grasping function, and it can not only perform linear-parallel pinching but also can grasp objects with different shapes, sizes in a stable way.