In this paper the sensing properties of SnO2 thin films, grown by the RGTO (rheotaxial growth and thermal oxidation) technique, towards low concentrations of H2S (100 ppb-10 ppm) are described. The RGTO method allows us to prepare thin films with a wrinkled surface, which is suitable for the dispersion of a metal catalyst in the form of small clusters. The catalytic effect of Pt, deposited on the film surface, towards the adsorption of hydrogen sulfide is examined in this paper. The maximum sensitivity DELTAG/G of these films towards 1 ppm of H2S is equal to 30 at 573 K, while the response and recovery times are equal to 20 and 80 s, respectively. Moreover, the selectivity towards H2S with respect to the other gases tested (H-2, CO, CH4, n-C4H10, ethyl alcohol, NO(x) and SO2) was increased with the deposition of the platinum layer. We present an investigation of the film surface made with STM and SEM and the structural analysis of the film obtained with an X-ray powder diffractometer. These results are correlated with the electrical responses of the sensor versus the dimension of the platinum clusters present on the film surface. The interaction mechanisms between H2S and the thin film surface are also discussed.