This invention aims at providing a catalyst body exhibiting a lower degradation of a catalyst due to thermal durability and capable of keeping higher catalyst performance for a long time. A catalyst component such as Pt is directly supported by Zr, W, etc, replacing elements inside a support such as Al of cordierite to provide a catalyst body without forming a coating layer. A combination of the catalyst component and the element inside the support is selected so that support strength is greater than 5 eV by simulation using a density functional method. Coarsening of catalyst particles can besuppressed and a high-performance catalyst body excellent in thermal durability can be obtained.