The present invention relates to a system and a method therefor capable of reducing the amount of heat which must be supplied to a regeneration tower for regenerating an absorbent in an acid gas capture system for such acid gas as carbon dioxide, and provides an acid gas capture system and an acid gas capture method capable of reducing energy consumption by using the heat from the system itself in an acid gas capture system. The system and method according to the present invention have the benefit of saving energy by lowering the thermal demand of a reboiler by using the low-temperature steam condensate generated in the capture system to cool the upper end of the regeneration tower and a steam generator and compressor.