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Grasping of complicated objects is an active research area which is developing fast throughout the years. Soft grippers can be an effective solution, since they are capable of holding workpieces of various shapes and interacting with unstructured environments effectively. Soft grippers generally consist of soft, flexible and compliant materials, which are able to conform to the shape of the object so that the gripper will not deform or bruise the soft object. Fast grasping of objects with various sizes and shapes remains a challenging task for soft grippers. In the present article, a soft gripper based on bi-stable dielectric elastomer actuator (DEA) inspired by the insect-catching ability of the Venus flytrap, is designed. This soft gripper can achieve good performances in grasping various objects by a simple actuation system. The gripper can switch from one stable state to another when subject to an impulse voltage of 0.04 s. The time duration for each grasping action is 0.17 s, and no continuous voltage is required for holding the gripped object. Thus, energy consumption can be achieved as low as 0.1386 J per grasping action. The mechanism of achieving bi-stable states is related to the duration of impulse voltage applied and the resonant frequency of the structure. The present study demonstrates that bi-stable dielectric elastomer actuators are capable of achieving fast speed for grasping with very low energy consumption, which is significant in the applications to soft grippers and biomimetic robots.