Microfluidic devices providing an accurate delivery of fluids at required rates are of considerable interest, especially for the biomedical field. The progress is limited by the lack of micropumps, which are compact, have high performance, and are compatible with standard microfabrication. This paper describes a micropump based on a new driving principle. The pump contains three membrane actuators operating peristaltically. The actuators are driven by nanobubbles of hydrogen and oxygen, which are generated in the chamber by a series of short voltage pulses of alternating polarity applied to the electrodes. This process guaranties the response time of the actuators to be much shorter than that of any other electrochemical device. The main part of the pump has a size of about 3 mm, which is an order of magnitude smaller in comparison with conventional micropumps. The pump is fabricated in glass and silicon wafers using standard cleanroom processes. The channels are formed in SU-8 photoresist and the membrane is made of SiNx. The channels are sealed by two processes of bonding between SU-8 and SiNx. Functionality of the channels and membranes is demonstrated. A defect of electrodes related to the lift-off fabrication procedure did not allow a demonstration of the pumping process although a flow rate of 1.5 µl/min and dosage accuracy of 0.25 nl are expected. The working characteristics of the pump make it attractive for the use in portable drug delivery systems, but the fabrication technology must be improved.