An apparatus and method for treating wastewater are provided. The method for treating wastewater includes: a pre-treatment step of removing impurities contained in high concentration wastewater and crushing the impurities using a crusher; a first aerobic treatment step of supplying wastewater containing organic acids to a first aerobic tank and injecting air to the first aerobic tank to be aerobically treated; an anaerobic treatment step of supplying the wastewater, from which excess organic acids are removed by the aerobic treatment, to an anaerobic tank to be anaerobically treated; a degassing step of supplying the wastewater treated in the aerobic and anaerobic treatment steps to a degassing tank to remove air and gas; and a post-treatment step of precipitating the wastewater aerobically treated using a solid-liquid separation tank, a pressure floatation tank or a precipitation tank.