A tape attaching apparatus includes: a chamber having an airtight space formed therein; a rubber sheet that partitions the airtight space into first and second airtight spaces and has an upper sheet on which a wafer is placed; a tape frame that holds a tape above the rubber sheet; and first and second supply/exhaust tubes that switch pressurization and depressurization of the first and second airtight spaces. In pressurizing the second airtight space and expanding the rubber sheet to lift the wafer to be attached to the tape, after bringing the first and second airtight spaces into a vacuum state, the wafer is attached to the tape while an amount of pressurization of the second airtight space is controlled to change an expansion rate of the rubber sheet from a low speed to a high speed stepwisely.