A plugged honeycomb structure including a honeycomb structure body, outflow side plugged portions, and inflow side plugged portions. A shape of cells in a cross section is a hexagonal shape. Among six corner portions of each of the hexagonal cells, the corner portion between two partition walls at least one of which is the partition wall separating inflow cells or outflow cells from each other is a specific corner portion, and the corner portion between the two partition walls each of which is the partition wall separating the inflow cell and the outflow cell is an unspecific corner portion. 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.