To provide a catalytic converter that reduces non-uniformity of temperature of a catalyst support and that can approach a uniform temperature distribution, and a structural body for supporting a catalyst that structures this catalytic converter. At a catalyst support, gradually decreasing width portions, at which a width thereof gradually decreases toward electrode centers, are formed at regions where electrodes, are contactingly disposed, as seen in a cross-section orthogonal to a direction in which exhaust flows. The width is shorter than a length of a center line at a given position. Heat generation and heat dissipation of the catalyst support are balanced overall.