The level measuring device (12) has a measuring tube (14) that is disposed in the fuel tank (10) and is filled by a partial flow of the fuel delivered to the injection system (44) of the engine (46) of the motor vehicle by a delivery unit (40) disposed in the fuel tank (10). On its one measurement input (26), a differential pressure sensor (24) is acted on by the hydrostatic pressure at the bottom end (30) of the measuring tube (14) and on its other measurement input (28), the sensor is acted on by the hydrostatic pressure at the bottom (16) of the fuel tank (10). When the delivery unit (40) is operating, a fuel column of a known height (lo) is produced in the measuring tube (14), so that the current level (h(t)) of the fuel tank (10) can be determined in an evaluation device (32) based on the output signal (u) of the differential pressure sensor (24). Close to its bottom end (30), the measuring tube (14) has an opening (56), through which the measuring tube (14) can be emptied, when the delivery unit (40) is switched off, to the point that the same level is set in it as in the fuel tank (10) and the offset of the differential pressure sensor (24) can be determined.