The invented tri-elemet purifying and catalytic agent are cornposed of non-noble metal complex carries directly on the surface of carrier with sillimanite and/or mullite as main matter phases. This invention also relates to the preparation method of stated carrier and catalyst and the application as tri-element purifying and catalytic agent for automobile tail gas and as combustion catalyst for industry organic waste gas combustion. Its features are that it has double performaces of catalysis and oxidization for carbon monoxide and hyolrocarbon and of catalysis and reduction for nitrogen oxide.