A high molecular weight polycarbonate resin is continuously produced by subjecting an aromatic polycarbonate prepolymer and an aliphatic diol compound to a linking and highly polymerizing reaction. Even an aliphatic diol compound having a comparatively low boiling point can be allowed to efficiently contribute to the linking and highly polymerizing reaction. An aromatic polycarbonate prepolymer is produced by a polycondensation reaction between an aromatic dihydroxy compound and a diester carbonate, adding an aliphatic diol compound having an aliphatic group bonding to a terminal hydroxyl group to obtain a prepolymer mixture, and subjecting the resulting prepolymer mixture to a linking and highly polymerizing reaction under reduced pressure. The aliphatic diol compound is added at a pressure exceeding 200 torr, and the prepolymer mixture is subjected to a linking and highly polymerizing reaction before the terminal hydroxyl group concentration of the aromatic polycarbonate prepolymer in the prepolymer mixture reaches 2000 ppm.