For data erase from an electrically erasable and programmable non-volatile memory cell, the following operations are performed: an erase operation to apply an erase pulse voltage to a memory cell for data erase, an erase verify operation to verify whether data erase is completed, and a step-up operation to increase the erase pulse voltage by a certain step-up voltage if data erase is not completed. A control unit controls voltages so that at least a first erase pulse voltage initially generated in the erase operation has a longer rise time than that of a second erase pulse voltage generated subsequent to the first erase pulse voltage.