The present invention relates to an apparatus and a method for treating wastewater by using an anaerobic separation membrane, which can reduce fouling of the separation membrane by re-circulating anaerobic sludge by means of a gravity drop method, which can apply biogas or carbon dioxide separated and extracted from the biogas to removal of fouling of the separation membrane, and which can maintain an anaerobic state by controlling pH and temperature of the re-circulated anaerobic sludge. According to the present invention, provided is the apparatus for treating wastewater by using an anaerobic separation membrane, the apparatus comprising: an anaerobic tank which converts raw water into anaerobic sludge by subjecting the raw water to an anaerobic process; an anaerobic separation membrane bioreactor which receives the anaerobic sludge from the anaerobic tank, and induces filtration of the corresponding anaerobic sludge by means of a separation membrane; the separation membrane which is provided inside the anaerobic separation membrane bioreactor, and performs a filtration process on the anaerobic sludge; a biogas collection part which collects biogas generated during the anaerobic processes in the anaerobic tank and the anaerobic separation membrane bioreactor; and a gas separation membrane which separates the biogas, collected in the biogas collection part, into methane (CH_4) and carbon dioxide (CO_2), wherein the anaerobic sludge is re-circulated between the anaerobic separation membrane bioreactor and the anaerobic tank, and the anaerobic sludge is moved from the anaerobic separation membrane bioreactor to the anaerobic tank by means of a gravity drop method.
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