Hot water or heated steam is fed to a drink supply pipe line 7 for simultaneously supplying drink to a plurality of filling nozzles 2a, while exhausting the hot water or heated steam from all the filling nozzles, F-values are calculated by detecting temperatures at a plurality of predetermined portions of the drink supply pipe line and all the filling nozzles at every predetermined time interval, and a sterilizing process is ended at a time when a minimum F-value reaches an aimed value. According to such method, the sterilization to the drink supply pipe line can be smoothly performed.