Individual tin dioxide nanobelts were used to fabricate field-effect transistor (FET) devices. The output characteristics of these devices have been measured under various ambient conditions, and modeled with a modified drift-diffusion model in which quantum mechanical effects are taken into consideration using the density-gradient model. It is shown that the saturation of the output curves (drain current versus drain-to-source voltage) in air is not due to channel pinch-off, but rather to the saturation of the reversed-biased current of the Schottky-like contact. In this case the source and drain contacts behave like rectifying diodes and can be modeled as two Schottky diodes connected back-to-back with a series resistance from the nanobelt separating the diodes. In the presence of hydrogen the rectifying behavior of the two contacts disappears and the current through the device is limited by the resistance of the nanobelt that can be modulated efficiently by using a gate electrode.