<p>A honeycomb catalyst structure (100) having opening-end-filling parts (10) each having a given length, wherein those planes of the parts (10) which are perpendicular to the direction of extension of cells (3) and are located inside the cells are uneven in position. A catalytic converter employing this honeycomb catalyst structure (100) has dispersed thermal stress and is inhibited from suffering a local temperature increase around the inlet and outlet. The converter is hence less apt to crack.</p>