H2S is a common component of natural gas. In order to meet the quality standards for U.S. commodity natural gas that contains less than 5.7 mg/m3 of H2S, it is necessary to process the natural gas to remove H2S. Since H2S will form azeotropes with ethane and propane in natural gas, it is impossible to achieve complete separation of H2S by ordinary distillation columns. Therefore, a novel low-temperature fractionation combined with extractive distillation process is proposed and designed, which can achieve the removal of H2S from sulfur-containing natural gas and obtain sweet gas(almost pure methane), ethane product and H2S gas. The process consists of three steps: demethanization with low temperature, deethanization with extractive distillation and H2S recovery. Extensive simulation and analysis have confirmed that extractive distillation using high molecular weight, high boiling point benzene homologs (toluene, o-Xylene, p-Xylene, m-Xylene) as extractant is a good method to separate ethane-H2S azeotrope. Furthermore, the effects of parameters such as the number of column stages, the reflux ratio, the location of feed stream inlet stage, the type of extractants, the inlet stage location of extractant, the molar flow rate of extractant on the product purity and the column duty have been studied, and the optimal applicable ranges of different parameters are finally determined. The simulation results show that o-Xylene is the best extractant for the separation of ethane and H2S. Under the economic optimization, the minimum total annual cost for the demethanizer is $952,611 per year and the minimum total annual cost for the deethanizer is $2,026,364 per year.