An aromatic polycarbonate resin is produced under the conditions that the flow velocity of the reaction mixture in a pipe through which a molten reaction mixture passes is a specific value or over, the viscosity-average molecular weight of the reaction mixture is 1,000 or more, the sum of the average retention times of the reaction mixture is not longer than 3 hours, the wall temperature of the pipe through which a molten reaction mixture passes is set to be higher than the temperature of the reaction mixture in the pipe, the catalyst deactivation agent is added within 2 hours after the completion of the melt polycondensation reaction, the filtration is carried out by using a filter having a specific retained particle size under a specific pressure difference, specific treated amount of the aromatic polycarbonate resin per unit area of the filter and a ratio of W (flow quantity of filtered polymer)×1,000/A (maximum area of the polymer path in the filtration vessel) falling within a specific range, etc.