Gripper is one of the most important parts of robot because of contacting with workpieces directly and has attracted lots of research interests. However, the existing grippers are either simple in function or complex in structure. In this paper, we will propose a one-DOF gripper based on a compliant mechanism with four identical twofold-symmetric Bricard linkages. A mobile network with four identical twofold-symmetric Bricard linkages with particular design parameters is constructed at first. Kinematics, such as mobility, singularity, and folding performance, is then analyzed to show the potential of realizing the function of grasping. The result is demonstrated with a physical prototype. To simplify the fabricating process, a compliant mechanism of the network is designed and fabricated with a single polypropylene board, and the grasping function is realized by a cable-driven scheme. Some grasping experiments are carried out on different types of objects which shows that the proposed and fabricated four-figure gripper is simple in structure and has a great grasping function. The work provides a new idea for the design of grippers with low cost, simple structure, and rich functions.