Among the configurations to generate plasma in electrically conductive liquids only the diaphragm and the capillary discharge schemes allow to generate plasma which is not in contact with one of the electrodes. Based on this concept, this work reports for the first time the development of an underwater plasma pump, in which the periodic electrical breakdown inside an asymmetrical (sub-)millimetre hole results in a net flow of aqueous solution through the hole without the use of any moving parts such as valves or diaphragms typically used in micropumps. Certain capillary geometries feature very stable flow rates and even allow altering flow direction by changing the power. By varying the hole's dimensions, the range of time-independent flow rates covers more than one order of magnitude and as the discharge produces some of the strongest oxidants available, we believe that this concept might find application in fields as water decontamination and sterilization.