A novel nanocatalyst is disclosed containing titanium oxide, iron oxide, and calcium oxide. The catalyst comprises a layer of iron oxide in the gamma form supported on a titanium oxide core. Addition of calcium cations helps to stabilize the iron oxide in the gamma form. The iron oxide layer is on the order of a few nanometers thick on the surface of the titanium oxide core, in an "egg-in-shell" structure. The nanocatalyst is highly active in promoting the oxidation of compounds such as hydroquinone, catechol, other hydrocarbons, chlorinated phenols, and carbon monoxide, even at moderately elevated temperatures. The catalyst remains active in a pyrolytic environment for extended periods of time, and possesses high redox cycling potential. The efficiency of the catalyst is not strongly affected by coking in a combustion environment. The catalyst may be used, for example, to reduce levels of radicals, catechols, dioxins, other toxic hydrocarbons, and carbon monoxide in cigarette smoke, incinerator waste streams, and waste streams from other, combustion sources. The catalyst operates efficiently at temperatures typical of tobacco smoke, is formed from nontoxic materials, and is relatively inexpensive. Methods of making and using the catalyst are also disclosed.