Odor emitted from food waste is commonly known as a severe problem, and needs to be controlled to minimize public complaints against food waste collection systems. In this study, ozone oxidation with manganese oxide catalyst, which is known to effectively treat odorous substances at room temperature, was applied to remove acetaldehyde and hydrogen sulfide, the model odorous compounds from food waste. In addition, the effect of relative humidity (RH) on the ozone/catalyst oxidation was tested at 40%, 60%, and 80%. When the catalyst was not applied, the removal of acetaldehyde was not observed with the ozone oxidation alone. In addition, hydrogen sulfide was slowly oxidized without a clear relationship under RH conditions. Meanwhile, the ozone oxidation rates for acetaldehyde and hydrogen sulfide substantially increased in the presence of the catalyst, but the removal efficiencies for both compounds decreased with increasing RH. Under the high RH conditions, active oxygen radicals, which were generated by ozone decomposition on the surface of the catalyst, were presumably absorbed and reacted with moisture, and the decomposition rate of the odorous compounds might be limited. Consequently, when the ozone oxidation device with a catalyst was applied to control odor from food waste, RH must be taken into account to determine the removal rates of target compounds. Moreover, its effect on the system performance must be carefully evaluated.