A method and to a device for the electrostatic separation of fine dust particles from gases that flow through a housing (1) containing perforated plates (6) and electrodes (4, 5). An electric field is created between the electrode (4) on the inflow opening side and the electrode or electrodes (5) having positive polarity on the outflow side. The removal of negatively charged fine dust particles (9) is carried out by deposition on the inflow side of the perforated plates (6), and the removal of positively charged fine dust particles (11) is carried out on the outflow side. Fine dust particles without charge (10) are charged after the last perforated plate (6) in an ionization chamber (8) and deposit on the outflow side of the last perforated plate (6).