In order to investigate the role of cosmic rays in the formation of methanol on dust grains, low-energy electron irradiation (similar to 10-300 eV) on mixed H2O/CH4 ice was studied by infrared (IR) spectroscopy and thermal desorption spectrometry (TDS). CH3OH was formed as a major product along with H2CO, C2H4, C2H6, and C2H2 as minor products when the mixed H2O/CH4 (10/1) ice was irradiated by electrons at 10K. There were found to be two pathways for the formation of methanol with about equal importance, i.e., the recombination reaction, CH3 + OH -> CH3OH, and the insertion reaction, CH2 + H2O -> CH3OH. One CH3OH molecule was formed per 60 electron irradiations with an electron energy of 100 eV. By using mixed H2O/CD4 ice, it was confirmed that formaldehyde was formed by the insertion reaction, C + H2O -> H2CO.