Interest in bioinspired peristaltic pumps has grown in popularity among the scientific community in the last decade thanks to their extreme flexibility and their intrinsic compliance. In this paper, we propose a soft peristaltic pump exploiting ballooning. Our aim is to promote and propel forward the ballooned region by controlling the air pressure between the balloon and an external flexible containment tube. Thanks to this mechanism, it is possible to achieve a peristaltic pumping motion with a simple design and using only one control signal. In this paper, we describe the implementation of the pump and the inlet-pump-outlet system, provide an analytical model to predict the pump performance, and experimentally test the device. Finally, the proposed pump is directly compared with the state-of-the-art. We show that it is possible to achieve high flow rates, up to 4.5 mL s , with only a single control signal and relying on a much simpler design, paving the way for more flexible and easy to manufacture peristaltic pumps.