A ceramic honeycomb structure having a plurality of flow paths partitioned by porous cell walls comprising cordierite, (a) said cell walls having porosity of more than 65% and 75% or less; and (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, said cumulative pore volume being cumulative volume of pores in a range from the maximum pore diameter to a particular pore diameter, a median pore diameter d50 at 50% being 18 μm or more and 27 μm or less, a pore diameter d90 at 90% being 10 μm or more, and (d10 - d90)/d50 being 2.3 or less; (ii) σ [= log - log] 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 S n = -(V n - V n-1)/[log(d n) - log(d n-1)] of a curve of a cumulative pore volume to a pore diameter being 3 or more, wherein d n and V n are respectively a pore diameter and a cumulative pore volume at an n-th measurement point, and d n-1 and V n-1 are respectively a pore diameter and a cumulative pore volume at a (n-1)-th measurement point. (a) said cell walls having porosity of more than 65% and 75% or less; and (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, said cumulative pore volume being cumulative volume of pores in a range from the maximum pore diameter to a particular pore diameter, a median pore diameter d50 at 50% being 18 μm or more and 27 μm or less, a pore diameter d90 at 90% being 10 μm or more, and (d10 - d90)/d50 being 2.3 or less; (ii) σ [= log - log] 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 S n = -(V n - V n-1)/[log(d n) - log(d n-1)] of a curve of a cumulative pore volume to a pore diameter being 3 or more, wherein d n and V n are respectively a pore diameter and a cumulative pore volume at an n-th measurement point, and d n-1 and V n-1 are respectively a pore diameter and a cumulative pore volume at a (n-1)-th measurement point. (i) a pore diameter d10 at a cumulative pore volume corresponding to 10% of the total pore volume being less than 50 μm, said cumulative pore volume being cumulative volume of pores in a range from the maximum pore diameter to a particular pore diameter, a median pore diameter d50 at 50% being 18 μm or more and 27 μm or less, a pore diameter d90 at 90% being 10 μm or more, and (d10 - d90)/d50 being 2.3 or less; a median pore diameter d50 at 50% being 18 μm or more and 27 μm or less, a pore diameter d90 at 90% being 10 μm or more, and (d10 - d90)/d50 being 2.3 or less; (ii) σ [= log - log] 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 S n = -(V n - V n-1)/[log(d n) - log(d n-1)] of a curve of a cumulative pore volume to a pore diameter being 3 or more, wherein d n and V n are respectively a pore diameter and a cumulative pore volume at an n-th measurement point, and d n-1 and V n-1 are respectively a pore diameter and a cumulative pore volume at a (n-1)-th measurement point.