Co-combustion of methane (CH4) and acid gas (AG) is required to sustain the temperature in Claus reaction furnace. In this study, oxy-fuel combustion of methane and acid gas has been experimentally studied in a diffusion flame. Three equivalence ratios (ER = 1.0, 1.5, 2.0) and CH4-addition ratios (CH4/AG = 0.3, 0.5, 0.7) were examined and the flame was interpreted by analyzing the distributions of the temperature and species concentration along central axial. CH4-AG diffusion flame could be classified into three sections namely initial reaction, oxidation and complex reaction sections. Competitive oxidation of CH4 and H2S was noted in the first section wherein H2S was preferred and both were mainly proceeding decomposition and partial oxidation. SO2 was formed at oxidation section together with obvious presence of H2 and CO. However, H2 and CO were inclined to be sustained under fuel rich condition in the complex reaction section. Reducing ER and increasing CH4/AG contributed to higher temperature, H2S and CH4 oxidation and CO2 reactivity. Hence a growing trend for CH4 and AG to convert into H2, CO and SO2 could be witnessed. And this factor enhanced the generation of CS2 and COS in the flame inner core by interactions of CH4 and CO2 with sulfur species. COS was formed through the interactions of CO and CO2 with sulfur species. The CS2 production directly relied on reaction of CH4 with sulfur species. The concentration of COS was greater than CS2 since CS2 was probably inhibited due to the presence of H2. COS and CS2 could be consumed by further oxidation or other complex reactions.