A filtering operation method for filtering fine crystals contained in an oxidation reaction mother liquor obtained in a process for producing an aromatic carboxylic acid except for terephthalic acid by a cross-flow filtration using a ceramic filter while conducting a flowing circulation operation of the oxidation reaction mother liquor, the method comprising: conducting an operation for filtering the fine crystals; conducting a back washing operation with a filtrate while maintaining the flowing circulation operation of the oxidation reaction mother liquor; and conducting a back washing operation with a wash solvent while maintaining the flowing circulation operation of the oxidation reaction mother liquor, the back washing operation with the filtrate being conducted under the following conditions: (II-A) an operation time thereof that is in the range of from 5 to 60 [s]; (II-B) a differential pressure between a filtration side and a flow path side of the ceramic filter which is in the range of from 0.10 to 1.0 [MPa]; (II-C) a feeding linear velocity of the filtrate that is in the range of from 1.0 to 20 [m/h]; and (II-D) a temperature of the filtrate that is in the range of from "a temperature of the oxidation reaction mother liquor" to "a temperature higher by 35°C than that of the oxidation reaction mother liquor", the back washing operation with the wash solvent being conducted under the following conditions: (III-A) an operation time thereof that is in the range of from 5 to 120 [s]; (III-B) a differential pressure between the filtration side and the flow path side upon the back washing operation with the wash solvent that is in the range of from 0.10 to 1.0 [MPa]; (III-C) a feeding linear velocity of the wash solvent upon the back washing operation that is in the range of from 1.0 to 20 [m/h]; and (III-D) a temperature of the wash solvent that is in the range of from "the temperature of the oxidation reaction mother liquor" to "the temperature higher by 35°C than that of the oxidation reaction mother liquor". conducting an operation for filtering the fine crystals; conducting a back washing operation with a filtrate while maintaining the flowing circulation operation of the oxidation reaction mother liquor; and conducting a back washing operation with a wash solvent while maintaining the flowing circulation operation of the oxidation reaction mother liquor, the back washing operation with the filtrate being conducted under the following conditions: (II-A) an operation time thereof that is in the range of from 5 to 60 [s]; (II-B) a differential pressure between a filtration side and a flow path side of the ceramic filter which is in the range of from 0.10 to 1.0 [MPa]; (II-C) a feeding linear velocity of the filtrate that is in the range of from 1.0 to 20 [m/h]; and (II-D) a temperature of the filtrate that is in the range of from "a temperature of the oxidation reaction mother liquor" to "a temperature higher by 35°C than that of the oxidation reaction mother liquor", (II-A) an operation time thereof that is in the range of from 5 to 60 [s]; (II-B) a differential pressure between a filtration side and a flow path side of the ceramic filter which is in the range of from 0.10 to 1.0 [MPa]; (II-C) a feeding linear velocity of the filtrate that is in the range of from 1.0 to 20 [m/h]; and (II-D) a temperature of the filtrate that is in the range of from "a temperature of the oxidation reaction mother liquor" to "a temperature higher by 35°C than that of the oxidation reaction mother liquor", the back washing operation with the wash solvent being conducted under the following conditions: (III-A) an operation time thereof that is in the range of from 5 to 120 [s]; (III-B) a differential pressure between the filtration side and the flow path side upon the back washing operation with the wash solvent that is in the range of from 0.10 to 1.0 [MPa]; (III-C) a feeding linear velocity of the wash solvent upon the back washing operation that is in the range of from 1.0 to 20 [m/h]; and (III-D) a temperature of the wash solvent that is in the range of from "the temperature of the oxidation reaction mother liquor" to "the temperature higher by 35°C than that of the oxidation reaction mother liquor". (III-A) an operation time thereof that is in the range of from 5 to 120 [s]; (III-B) a differential pressure between the filtration side and the flow path side upon the back washing operation with the wash solvent that is in the range of from 0.10 to 1.0 [MPa]; (III-C) a feeding linear velocity of the wash solvent upon the back washing operation that is in the range of from 1.0 to 20 [m/h]; and (III-D) a temperature of the wash solvent that is in the range of from "the temperature of the oxidation reaction mother liquor" to "the temperature higher by 35°C than that of the oxidation reaction mother liquor".