In this paper, a simulated “soft” mechanical grasper (GXU-Grasper) with self-locking capability, self-adaptive object shape, single-degree of actuation, and full rigid structure is taken as the research object, and its self-adaptive grasping is analyzed. First, the degrees-of-freedom of the knuckle unit and the fingers of the grasper are calculated. Then, the kinematic model of finger self-adaptive grasping is established by the homogeneous coordinate matrix method. The joint motion space model of grasper under different component parameters is established. Based on this analysis, the corresponding grasping workspace formed by the grasper under different component motion parameters is given by numerical analysis in combination with the grasper finger kinematic model. Finally, the adaptive grasping experiment of the GXU-Grasper is carried out. The experiment shows that the fingers of the GXU-Grasper can effectively grasp various irregular objects in its workspace with relatively strong adaptability and large grasping range, which provides a reference for further analysis of the grasping reliability and engineering application of this grasper.