A porous ceramic structure includes a porous honeycomb structure composed primarily of cordierite, and Ce- and Zr-containing particles fixedly attached to the honeycomb structure. The Ce- and Zr-containing particles contain Ce and Zr. The Ce- and Zr-containing particles have a fixedly attached portion located inside the honeycomb structure and a protrusion contiguous with the fixedly attached portion and protruding from the honeycomb structure.