This paper proposes a shape-adaptive electroadhesion dielectric elastomer actuator (EA-DEA) pad gripper that can actively adapt to the shape of curved objects and quickly handle various objects by combining an EA pad and a multi-layered DEA driven by electrostatic force. This gripper has a rapid release function capable of detaching thin and light objects in less than 0.2 s with bending motion of multi-layered DEA and reverse polarity voltage. Moreover, combined with a transform mechanism that changes the posture of the EA-DEA pad gripper, a multifunctional gripper handling various objects from thin to irregularly shaped objects is implemented. The high voltage controller is configured to generate the variable and reversible voltages required for the control of the developed gripper. To verify the performance and practicality of the proposed multifunctional gripper system, we demonstrate the gripping task in three modes formed by controlling the EA-DEA pad gripper and the transform mechanism to adapt to the object shape. According to the experimental results, this gripper can reliably and rapidly pick and place various objects, such as thin film, hexahedron, cylinders, spheres, irregular shaped, deformable, and fragile objects corresponding to each mode.