To provide a hexagonal cell honeycomb structure which can make an early activation of a catalyst, improve the cleaning performance of an exhaust gas by a catalyst and reduce pressure loss, while securing a practically enduring strength.

This hexagonal cell honeycomb structure 1 includes a hexagonal lattice-like cell wall 2, many number of hexagonal cells 3 surrounded by the cell wall 2 and a cylindrical skin layer 4 covering the outer circumferential side surface. The average thickness of a basic cell wall 2a of the cell wall 2 is not more than 140 m, and the relationship between the mean value Dax of the diameter Da of a circle in contact with the profile of three cell openings at a mutual intersection part of the three basic cell walls 2a, and the cell pitch P, is Dax/P0.13. In addition, the surface 20a of the basic cell wall 2a is formed denting inward like a curve on the cross-section of the hexagonal cell honeycomb structure 1. Further, the inside corner part 29a which is formed by the adjacent two basic cell walls 2a, is formed like a curve so that the inside corner part 29a can smoothly connect the surfaces 20a of the two basic cell walls 2a.