A plugged honeycomb structure comprising: a honeycomb structure body having porous partition walls with which a plurality of cells extending from an inflow side end surface to an outflow side end surface are formed to define through channels of a fluid; outflow side plugged portions arranged in open frontal areas of the predetermined cells at the outflow side end surface; and inflow side plugged portions arranged in open frontal areas of the remaining cells at the inflow side end surface, wherein the shape of the cells in a cross section perpendicular to an extending direction of the cells is hexagonal, and when among six corner portions of each of the hexagonal cells (42,62), the corner portion between two sides which are the two partition walls (41,61) constituting the corner portion and at least one of which is the partition wall separating two inflow cells (42a,62a) or separating two outflow cells (42b,62b) from each other is a specific corner portion (55a,75a), and the corner portion between two sides which are the two partition walls constituting the corner portion and each of which is the partition wall separating the inflow cell (42a,62a) and the outflow cell (42b,62b) is an unspecific corner portion (55b,75b), the inflow cells (42a,62a) being open at the inflow side end surface (51,71) and being plugged with the outflow side plugged portions (45b,65b) at the outflow side end surface (52,72), the outflow cells (42b,62b) being open at the outflow side end surface (52,72) and being plugged with the inflow side plugged portions (45a,65a) at the inflow side end surface (51,71), at least one of the specific corner portions (55a,75a) is provided with a reinforcing portion (46,66) so that a shape of the specific corner portion (55a,75a) is rounded, and the unspecific corner portions (55b,75b) are not provided with the reinforcing portions; wherein only the specific corner portions (55a,75a) of the outflow cells (42b,62b) are provided with the reinforcing portions (46,66) and only the specific corner portions (55aa,75aa) between two sides which are the partition walls separating two inflow cells (42a,62a) or separating two outflow cells (42b,62b) from each other are provided with the reinforcing portion; wherein in the cross section of the honeycomb structure body which is perpendicular to the cell extending direction, 70% or more of the specific corner portions provided with the reinforcing portions are present in a region of a length from an outer peripheral edge of the honeycomb structure body in a normal direction of the outer peripheral edge, the length corresponding to the length of 1/3 or less of a length of a long axis of the outer peripheral edge. a honeycomb structure body having porous partition walls with which a plurality of cells extending from an inflow side end surface to an outflow side end surface are formed to define through channels of a fluid; outflow side plugged portions arranged in open frontal areas of the predetermined cells at the outflow side end surface; and inflow side plugged portions arranged in open frontal areas of the remaining cells at the inflow side end surface, wherein the shape of the cells in a cross section perpendicular to an extending direction of the cells is hexagonal, and when among six corner portions of each of the hexagonal cells (42,62), the corner portion between two sides which are the two partition walls (41,61) constituting the corner portion and at least one of which is the partition wall separating two inflow cells (42a,62a) or separating two outflow cells (42b,62b) from each other is a specific corner portion (55a,75a), and the corner portion between two sides which are the two partition walls constituting the corner portion and each of which is the partition wall separating the inflow cell (42a,62a) and the outflow cell (42b,62b) is an unspecific corner portion (55b,75b), the inflow cells (42a,62a) being open at the inflow side end surface (51,71) and being plugged with the outflow side plugged portions (45b,65b) at the outflow side end surface (52,72), the outflow cells (42b,62b) being open at the outflow side end surface (52,72) and being plugged with the inflow side plugged portions (45a,65a) at the inflow side end surface (51,71), at least one of the specific corner portions (55a,75a) is provided with a reinforcing portion (46,66) so that a shape of the specific corner portion (55a,75a) is rounded, and the unspecific corner portions (55b,75b) are not provided with the reinforcing portions; wherein only the specific corner portions (55a,75a) of the outflow cells (42b,62b) are provided with the reinforcing portions (46,66) and only the specific corner portions (55aa,75aa) between two sides which are the partition walls separating two inflow cells (42a,62a) or separating two outflow cells (42b,62b) from each other are provided with the reinforcing portion; wherein in the cross section of the honeycomb structure body which is perpendicular to the cell extending direction, 70% or more of the specific corner portions provided with the reinforcing portions are present in a region of a length from an outer peripheral edge of the honeycomb structure body in a normal direction of the outer peripheral edge, the length corresponding to the length of 1/3 or less of a length of a long axis of the outer peripheral edge.