Disclosed is a pneumatic membrane gasometer for the storage of hydrogen gas at low pressure. The gasometer includes: a first bag-shaped membrane delimiting a hydrogen storage chamber; a second membrane partially delimiting a pressurization chamber superimposed, at least in part, on the storage chamber; a third membrane, placed resting on top of the first membrane, fixed in an impermeable manner at least to the second membrane, defining, with the first membrane, a cavity open towards the outside of the gasometer; hydrogen supply and discharge unit associated with the storage chamber; pressurization unit; mechanical anchor to a base surface of the first, second and third membranes; and a natural passive ventilation system to vent any hydrogen losses to the outside, including a duct adapted to connect cavity to the outside environment passing through the pressurization chamber.