A ceramic honeycomb structure having a plurality of partition walls partitioning a plurality of cells extending in an axial direction, wherein at least a part of consecutive partition walls having a curved shape protruding either (a) toward outside from the centre of a cross-section perpendicular to the axial direction, such that the central portion has a lower cell density than the outer peripheral portion; or (b) toward the centre of a cross-section perpendicular to the axial direction from outside the cross-section, such that the central portion has a higher cell density than the outer peripheral portion; consecutive partition walls being defined: (i) in the case that the basic shape of the cross-section of a cell is one for which the partition walls are continuous from one point on the outer peripheral wall of the honeycomb structure to another point on the outer peripheral wall to form a smooth line, that is, a line without a bent point in a cross-section of the honeycomb structure; partition walls forming one line continuous from said one point on the outer peripheral wall to said another point on the outer peripheral wall being defined as a consecutive partition wall; whereby a curvature can be determined from a width of deviation of the line which the consecutive partition wall forms from the straight line connecting said one point on the outer peripheral wall to said another point on the outer peripheral wall; (ii) in the case that the basic shape of the cross-section of a cell is one for which partition walls do not form a smooth line continuous from one point on the outer peripheral wall to another point on the outer peripheral wall, partition walls forming a broken line continuous from one point on the outer peripheral wall of the honeycomb structure to another point on the outer peripheral wall without a bent point are defined as a consecutive partition wall; whereby a curvature can be determined from a width of deviation of the line which the consecutive partition wall forms from the straight line connecting said one point on the outer peripheral wall to said another point on the outer peripheral wall; and wherein an average curvature of the consecutive partition walls is 0.6 ≤ Wav (mm) ≤ 15; the average curvature being the average value of width (Wn) of the maximum deviation of each of the consecutive partition walls (n) from a straight line, the average curvature Wav in the case that a honeycomb structure is provided with 1 to n consecutive partition walls being expressed by the following formula: Wav = W 1 + W 2 + W 3 + ⋯ + Wn / n. (a) toward outside from the centre of a cross-section perpendicular to the axial direction, such that the central portion has a lower cell density than the outer peripheral portion; or (b) toward the centre of a cross-section perpendicular to the axial direction from outside the cross-section, such that the central portion has a higher cell density than the outer peripheral portion; (i) in the case that the basic shape of the cross-section of a cell is one for which the partition walls are continuous from one point on the outer peripheral wall of the honeycomb structure to another point on the outer peripheral wall to form a smooth line, that is, a line without a bent point in a cross-section of the honeycomb structure; partition walls forming one line continuous from said one point on the outer peripheral wall to said another point on the outer peripheral wall being defined as a consecutive partition wall; whereby a curvature can be determined from a width of deviation of the line which the consecutive partition wall forms from the straight line connecting said one point on the outer peripheral wall to said another point on the outer peripheral wall; (ii) in the case that the basic shape of the cross-section of a cell is one for which partition walls do not form a smooth line continuous from one point on the outer peripheral wall to another point on the outer peripheral wall, partition walls forming a broken line continuous from one point on the outer peripheral wall of the honeycomb structure to another point on the outer peripheral wall without a bent point are defined as a consecutive partition wall; whereby a curvature can be determined from a width of deviation of the line which the consecutive partition wall forms from the straight line connecting said one point on the outer peripheral wall to said another point on the outer peripheral wall; and wherein an average curvature of the consecutive partition walls is 0.6 ≤ Wav (mm) ≤ 15; the average curvature being the average value of width (Wn) of the maximum deviation of each of the consecutive partition walls (n) from a straight line, the average curvature Wav in the case that a honeycomb structure is provided with 1 to n consecutive partition walls being expressed by the following formula: Wav = W 1 + W 2 + W 3 + ⋯ + Wn / n.