A hexagonal-cell honeycomb catalyzer is for purifying an exhaust gas. The catalyzer comprising a support that has a plurality of cells and a purification layer that has an HC absorption layer and a three-way catalyst layer. The HC absorption layer is formed on the honeycomb-formed surface of each wall of the support. The three-way catalyst layer is formed on the surface of the HC absorption layer. Provided that the HC absorption layer has a thickness a1 and the three-way catalyst layer has a thickness b1 at a thin portion of the purification layer of which thickness is minimum and the HC absorption layer has a thickness a2 and the three-way catalyst layer has a thickness b2 at a thick portion of the purification layer of which thickness is maximum, a ratio of a1/b1 and a ratio of a2/b2 are both within a range of 1/20 to 5/1.