Sour gas is a special type of natural gas that contains H2S and takes a large percentage of present natural gas reserves. Facing the increasing world energy demand, direct combustion of sour gas has been proposed as a potential choice, which requires systematic investigations on the sour gas combustion characteristics. In this work, the laminar burning velocities SL of 85% CH4 + 15% H2S + N2 + O2 and CH4 + N2 + O2 flames were measured using the heat flux method at 1 atm and 298 K, where the oxygen ratio xO2 and equivalence ratio ϕ ranges covered 0.17–0.24 and 0.7–1.4, respectively. Part of the conditions have never been reported before in the literature, and the SL tendencies against all the three dimensions of ϕ, xO2, xH2S were systematically compared. Simulations using the Mulvihill mechanism were carried out, showing good agreement with all the experimental data measured. By the kinetic analyses including maximum flame temperatures, reaction sensitivities, reaction paths, and maximum mole fractions of key radicals, distinct kinetic features of the fuel-rich CH4 + H2S + N2 + O2 flames were found, which are different from the lean and stoichiometric flames. S-containing products in the CH4 + H2S + N2 + O2 flames were also discussed using the simulation results. Besides the most dominant SO2 among all the conditions investigated in the present study, it’s noticed that the formation of the element sulfur, especially S2, is enhanced at fuel-rich conditions with small xO2. This phenomenon can be helpful for the design of real applications as the S2 particles can be easily condensed and reduce the load of desulfurization.