In this study, a Cu-promoted Fe/ZSM-5 catalyst was examined to reveal the effects of Cu species in selective oxidation of methane into methane oxygenates using H2O2 in water. Cu/ZSM-5, Cu-Fe/ZSM-5, and Fe/ZSM-5 catalysts were prepared using wet impregnation, solid-state ion exchange, and ion-exchange methods. Various techniques, including nitrogen physisorption, temperature-programmed reduction with H2, UV-vis spectroscopy, and FT-IR spectroscopy after NO adsorption, were utilized to characterize the catalysts. The promotional effect of Cu on the Cu-Fe/ZSM-5 catalyst in terms of methanol selectivity was confirmed. The preparation method has a considerable influence on the catalyst performance, and the ion-exchange method is the most effective. However, leaching of the Cu species was observed during this reaction, which can affect the quantification of formic acid by 1H-NMR. The homogeneous Cu species increase hydrogen peroxide decomposition and CO2 selectivity, which is undesirable for this reaction.