To provide information on the conversion of methane in a non-catalyzed radio-frequency (RF) plasma system into valuable chemicals, such as HCHO, CH3OH, C2H6, C2H4 and C2H2, an experiment was conducted to convert methane directly into methanol and formaldehyde. The effects of experimental parameters—specific energy (power or flow variation) and CH4 and O2 feeding concentrations—were examined. Carbon-based by-products generated in a CH4/O2/Ar RF plasma system included CO, CO2, HCHO, CH3OH, C2H6, C2H4 and C2H2. The methane conversion ratio increased as the feeding concentration of O2 and the specific energy was increased, but decreased with feeding of CH4. Increasing power in the RF plasma system did not favor the partial oxidation of CH4 toward CH3OH and HCHO, but did favor the production of C2-hydrocarbons (C2H6, C2H4 and C2H2), CO, and CO2. The CH4 feeding concentration of under 15% or an O2 content of under 10% favored the formation of CH3OH and HCHO. CO concentration decreased as the feeding concentration of CH4 increased, and increased as the feeding concentration of O2 increased. The yield of CH3OH was less than 1%. No carbon black or deposition was observed. Further research will seek to increase the yield of CH3OH and HCHO by adding catalysts to the system.