Reaction F + H2S®SH + HF (1) is an effective source of SH radicals, an important intermediate in atmospheric and combustion chemistry. We employed a discharge-flow, modulated molecular beam mass spectrometry technique to determine the rate coefficient of this reaction and that of the secondary one, F + SH®S + HF (2), at a total pressure of 2 Torr and in a wide temperature range 220–960 K. The rate coefficient of Reaction (1) was determined directly by monitoring consumption of F atoms under pseudo-first-order conditions in an excess of H2S. The rate coefficient of Reaction (2) was determined via monitoring the maximum concentration of the product of Reaction (1), SH radical, as a function of [H2S]. Both rate coefficients were found to be virtually independent of temperature in the entire temperature range of the study: k1 = (1.86 ± 0.28) × 10−10 and k2 = (2.0 ± 0.40) × 10−10 cm3 molecule−1 s−1. The kinetic data from the present study are compared with previous room temperature measurements.