A honeycomb filter is provided comprising a honeycomb structure having a large number of through channels formed in an axial direction and partitioned by porous partition walls, each of the through channels having a first end at one end of the filter and a second end at an opposite end of the filter, wherein a first group of the through channels are plugged only at the first end, and a second group of the through channels are not plugged. A honeycomb structure is further provided having through channels with a relatively large frontal area and through channels with a relatively small frontal area, and wherein all the through channels with a relatively large frontal area are the first group, and all the through channels with a relatively small frontal area are in the second group. A honeycomb filter is also provided with a catalyst component carried on a surface of the partition walls and/or a surface of pores present in an inside of the partition walls.