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, the corner portion between two sides which are the two partition walls constituting the corner portion and at least one of which is the partition wall separating two inflow cells or separating two outflow cells from each other is a specific corner portion, 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 and the outflow cell is an unspecific corner portion, the inflow cells being open at the inflow side end surface and being plugged with the outflow side plugged portions at the outflow side end surface, the outflow cells being open at the outflow side end surface and being plugged with the inflow side plugged portions at the inflow side end surface, at least one of the specific corner portions is provided with a reinforcing portion so that a shape of the specific corner portion is rounded, and the unspecific corner portions are not provided with the reinforcing portions; wherein the ratio of the number of the specific corner portions provided with the reinforcing portions to the number of the specific corner portions is 10% or more and 80% or less. 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, the corner portion between two sides which are the two partition walls constituting the corner portion and at least one of which is the partition wall separating two inflow cells or separating two outflow cells from each other is a specific corner portion, 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 and the outflow cell is an unspecific corner portion, the inflow cells being open at the inflow side end surface and being plugged with the outflow side plugged portions at the outflow side end surface, the outflow cells being open at the outflow side end surface and being plugged with the inflow side plugged portions at the inflow side end surface, at least one of the specific corner portions is provided with a reinforcing portion so that a shape of the specific corner portion is rounded, and the unspecific corner portions are not provided with the reinforcing portions; wherein the ratio of the number of the specific corner portions provided with the reinforcing portions to the number of the specific corner portions is 10% or more and 80% or less.