A cordierite-type ceramic honeycomb structure having large numbers of flow paths partitioned by porous cell walls; the cell walls having (a) porosity of more than 65% and 75% or less, (b) in a pore diameter distribution measured by mercury porosimetry, (i) a pore diameter d10 at a cumulative pore volume corresponding to 10% of the total pore volume being less than 50 μm, a pore diameter (median pore diameter) d50 at 50% being 18-27 μm, a pore diameter d90 at 90% being 10 μm or more, and (d10−d90)/d50 being 2.3 or less; (ii) σ [=log(d20)−log(d80)] being 0.25 or less, wherein σ represents the difference between a logarithm of a pore diameter d20 at a cumulative pore volume corresponding to 20% of the total pore volume and a logarithm of a pore diameter d80 at a cumulative pore volume corresponding to 80% of the total pore volume; and (iii) the maximum of the inclination Sn=−(Vn−Vn-1)/[log(dn)−log(dn-1)] of a curve of a cumulative pore volume to a pore diameter being 3 or more, wherein dn and Vn are respectively a pore diameter and a cumulative pore volume at an n-th measurement point, and dn-1 and Vn-1 are respectively a pore diameter and a cumulative pore volume at a (n−1)-th measurement point.