Provided is a simple filtering operation method capable of conducting a filtering operation without clogging in a ceramic filter for a long period of time, in the operation of filtering fine crystals of terephthalic acid in an oxidation reaction mother liquor obtained in a process of terephthalic acid production by a cross-flow filtration using the ceramic filter. The present invention can be accomplished by conducting an operation for filtering the fine crystals and a back washing operation with a filtrate while maintaining a flowing circulation operation of the oxidation reaction mother liquor under predetermined conditions.