Designing and manufacturing actuators using soft materials are among the most important subjects for future robotics. In nature, animals made by soft tissues such as the octopus have attracted the attention of the robotics community in the last years. Suckers (or suction cups) are one of the most important and peculiar organs of the octopus body, giving it the ability to apply high forces on the external environment. The integration of suction cups in soft robots can enhance their ability to manipulate objects and interact with the environment similarly to what the octopus does. However, artificial suction cups are currently actuated using fluid pressure so most of them require external compressors, which will greatly increase the size of the soft robot. In this work, we proposed the use of the ElectroHydroDynamics (EHD) principle to actuate a suction cup. EHD is a fluidic phenomenon coupled with electrochemical reaction that can induce pressure through the application of a high-intensity electric field. We succeeded in developing a suction cup driven by EHD keeping the whole structure extremely simple, fabricated by using a 3D printer and a cutting plotter. We can control the adhesion of the suction cup by controlling the direction of the fluidic flow in our EHD pump. Thanks to a symmetrical arrangement of the electrodes, composed by plates parallel to the direction of the channel, we can change the direction of the flow by changing the sign of the applied voltage. We obtained the pressure of 643 Pa in one unit of EHD pump and pressure of 1428 Pa in five units of EHD pump applying 6 kV. The suction cup actuator was able to hold and release a 2.86 g piece of paper. We propose the soft actuator driven by the EHD pump, and expand the possibility to miniaturize the size of soft robots.