This study was conducted to find a catalyst system which has high conversion and selectivity for the oxidative coupling of methane to produce ethane and ethylene. Various catalysts were tested in a fixed bed reactor ar 750℃, 1 atm, and the feed ratio(CH4/O2) of 2/1. Under the reaction condition, 10wt%PbSO4/MgO catalyst showed the highest catalytic activity : methane conversion, C2 selectivity and yield were 50, 40 and 20%, respectively. Catalysts containing sulfate compounds, 10wt%PbSO4/MgO, 10wt%MgSO4/MgO and Na2SO4/MgO revealed a moderate methane conversions such as 38, 50 and 50%, respectively and low C2 selectivities such as 18, 5 and 9%, respectively. Catalysts containing carbonate compounds, 10wt%PbCO3/MgO, 10wt%Li2CO3/MgO and NaCO3/MgO, also showed a moderate methane conversions such as 64, 44 and 51%, respectively and low C2 selectivities such as 5, 6 and 2%, respectively. With the existence of chlorine and mercury, C2 selectivity was decreased.