In this paper, an origami-inspired deployable robotic grasper with two finger is presented, which can be used to grasp unknown objects of different shapes and sizes. By splitting the waterbomb crease pattern and then recombining the divided parts, a novel symmetrical crease pattern is obtained. To achieve the lightweight design of the robotic gripper, a truss structure is employed for the origami mechanism, wherein the creases and edges are configured as rods, and the vertices are designed as composite hinges. The composite hinge at each vertex is meticulously designed to ensure that the axes of all moving pairs intersect at a single point. This design ensures complete equivalence between the origami mechanism and the origami model, thereby simplifying both the geometric and kinematic analyses of the mechanism. Through the geometric analysis of origami unit, the input value range is obtained. Furthermore, kinematic analysis of the grabber is conducted to obtain the capture diameter and envelopment angle of the grabber under various input conditions. Finally, the adaptability of the robot during grasping tasks was evaluated, and the results demonstrate that the grasper can adapt to a variety of object shapes and sizes.