A monolithic ceramic filter having a portion of the partition wall of a honeycomb structure exposed with its end face on an outer wall surface of the structure and increased in thickness as compared to the remaining portion of the partition wall to form a flow resistance relaxing portion is disclosed. The monolithic ceramic filter may also have a groove-shaped recess which is separated via a partition from a liquid supply passage of a honeycomb structure and is in communication with the outside of the structure. The flow resistance of the filtrate within the partition walls may be diminished to enable efficient filtration. The filter is produced simply by extrusion molding. There is no necessity of forming holes for discharging the filtrate in some cases.