In this paper, we show in a series of experiments on 10 nm thick SnS thin film-based back-gate transistors that in the absence of the gate voltage, the drain current versus drain voltage (I _D-V _D) dependence is characterized by a weak drain current and by an ambipolar transport mechanism. When we apply a gate voltage as low as 1 μV, the current increases by several orders of magnitude and the I _D-V _D dependence changes drastically, with the SnS behaving as a p-type semiconductor. This happens because the current flows from the source (S) to the drain (D) electrode through a discontinuous superficial region of the SnS film when no gate voltage is applied. On the contrary, when minute gate voltages are applied, the vertical electric field applied to the multilayer SnS induces a change in the flow path of the charge carriers, involving the inner and continuous SnS layer in the electrical conduction. Moreover, we show that high gate voltages can tune significantly the SnS bandgap.