We introduce a soft actuator for grippers using DEA capable of bending actuation. The actuator is also able to generate the electro-adhesion by the fringe field formed at the edges of the electrodes. The adhesion improves the holding force and ensures the conformation of the structure to the object. After the characterization of the actuator, we develop a 2-finger soft gripper capable of holding various objects. The gripper has a mass of around 1 g, and consists of a few cm long actuation parts, realizing simple open-close movement. The compliance of the gripper leads to conformation of the structure against the object surface, which is proven by successful handling of objects with different geometries such as a toothbrush, a flat paper, and a ping pong ball. The effect of the electro-adhesion is visible when the paper is held with its flat shape meaning that an adhesion force against gravity exists. Also, by the fact that the conformed structure increases the contact area, the holding force is improved while avoiding damaging the object, which is highlighted by the ability to hold a raw egg weighing around 60 g. This soft gripper, combining both actuation and electro-adhesion, illustrates the potential use of DEA for soft robotics.