A refresh control apparatus is provided which is capable of dispersing a peak current at an all-bank refresh mode and reducing the characteristic difference between the banks. The refresh control apparatus includes an internal refresh counter for outputting row address signals to select word lines when a refresh command is inputted from an external circuit, a row decoder for outputting row decoding signals to select all banks in response bank active signals and the row address signals, an enable signal control unit for sequentially outputting at a time interval sense amplifier enable signals in response to the bank active signals and the refresh command, and a sense amplifier for sequentially refreshing all of the banks at a time interval in response to the sense amplifier enable signals.