A column shaped filter having a honeycomb structure including a number of through holes extending parallel with one another in the length direction with wall portion interposed therebetween. The through holes are constituted by large-capacity through holes having a relatively larger cross-sectional area in the cross section perpendicular to the length direction and small-capacity through holes having a relatively smaller cross-sectional area in the cross section. The numbers of the two types of through holes are substantially set to the same. The large-capacity through holes are sealed at one end of the filter, while the small-capacity through holes are sealed at the other end of the filter. The large-capacity and small-capacity through holes have a ratio of partition wall length, α, and an aperture ratio, β, and α and β satisfy β≧(20/9)α2+1 (where 0