There are provided a ceramic filter containing at least one functional material, a method of manufacturing the ceramic filter, a ceramic filter whose surface through which a liquid to be purified flows in is closest and the average particle size of the filter continuously increases toward the interior thereof with costs such as material cost and the like being low, a method of manufacturing the ceramic filter, a extrusion molding die used to manufacture the ceramic filters and an extrusion molding apparatus using the die. In the ceramic filer containing the functional material and the porous ceramic filter, the average particle size of the fine particles forming the filters continuously increases from at least one surface of the filters toward the interior thereof. A material compound containing material fine particles and a binder as well as the functional material when necessary are formed to the ceramic filter. At the time, molding is executed while applying ultrasonic vibration to at least one surface of a molded product or closely pressing it. To manufacture the above ceramic filters, ultrasonic vibrators and a close press means are disposed to at least a portion of an extrusion molding die.