Sorption and desorption behavior of a minor amount of H2S (190 ppm) contained in methane on a new kind of sorbent was experimentally studied by a dynamic method. The sorbent consists of a carrier (silica gel) and a stationary phase (the film of triethanolamine, TEA), which spreads outside the carrier granules. Breakthrough curves of H2S passed over an adsorber filled with the sorbent were measured at ambient temperature and different pressures. It was shown that the TEA film considerably enhanced the H2S sorption capacity, and the capacity is quite sensitive to the total pressure of the gas phase; therefore, saturated sorbent can be regenerated merely by releasing pressure at ambient temperature. On the basis of the study, a new cost competitive technology of sweetening natural gas might be developed.