In this paper, we report on design, modelling and construction of a simple continuous nuclear gauge for measuring the fluid levels in vessels. In this instrument, a point source and a point detector are used on top and bottom sides of the vessel. The theoretical framework that is needed for analyzing the instrument data is described and it is shown that with this type of design, any unknown systematic error during the measurements can be removed. The developed theoretical relations and the instrument modelling by the MCNPX code, demonstrate its linear response in the entire measuring span. By using a cesium-137 gamma radiation source and a NaI (Tl) scintillation detector in the construction of the nuclear level gauge, the linear response of the instrument is also experimentally confirmed. It is shown that the mean relative error in determination of water level in the entire range of an 85 cm height vessel was less than 3.57%, which is reasonably acceptable for this simple design.