This invention relates to a complex oxide combustion catalyst wherein the active components of complex oxide is carried directly on the carrier with sillimanite and/or mullite as main matter phases. The preparation method of catalyst includes metal salt-water solution dipped carrier prepared according to metal elements and its mole ratio which are needed by the active components, then it is dried, roasted and activited. This invention relates also to the preparation method of above stated carrier and the complex oxide combustion catalyst as combustion calalyst for catalyzing combustion, purifying and saving energy in the industry and civil use organic waste gas included carbon monoxide smoke.