When the under-actuated hand pinches the object on the worktable, the trajectory of the end of the finger is not a straight line, which makes it difficult for the hand to grasp the object from its both sides. In order to overcome this shortcoming, this paper proposes a new configuration of the linear-parallel and self-adaptive under-actuated hand which uses the four-link and sliding base mechanism to compensate for the vertical displacement of the end of the finger. Based on this new configuration, the mechanical structure of the under-actuated hand is designed, which has five degrees of freedom (DOFs), and is mainly composed of two fingers, a sliding base, four link compensation mechanisms and an outer base. These two fingers have exactly the same structure and size, where each finger uses only one motor to control two joints of the finger which realizes the under-actuated function. Through the cooperation of the four-link and sliding base mechanism, the under-actuated hand can realize the linear-parallel and self-adaptive hybrid grasping mode. Kinematics analysis and contact force analysis of the under-actuated hand are discussed, and the prototype of the under-actuated hand is developed to carry out the grasping experiments. The results of the simulation and experiment all show that the under-actuated hand has good motion performance and grasping stability and can be used as an end effector for intelligent robots.