A hexagonal cell honeycomb structure body has a plurality of hexagonal cells. Each hexagonal cell is surrounded by six cell walls in a hexagonal lattice shape. A R-shaped corner part of an approximate circular-arc shape is alternately formed at interior angle parts of the six cell walls forming each hexagonal cell. The three R-shaped corner parts are at the alternate internal corners of each hexagonal cell observed from a cross section of the axis direction of the hexagonal cell honeycomb structure body. A radius of curvature of each R-shaped corner part is larger than that of the interior corner part having no R-shaped corner part. The minimum radius of curvature of the R-shaped corner part is 2.8 to 5 times of a thickness of each hexagonal cell wall, namely within a range of 0.25 mm to 0.45 mm.