NOVELTY - External anaerobic membrane bioreactor comprises anaerobic pool (1) and several vertical pipe membrane assemblies (2) arranged in parallel and each comprises several pipe ultrafiltration membrane elements (3). The lower part of anaerobic pool is provided with water inlet (4) while its upper part is provided with water outlet (9). First water inlet pipe (10) is arranged between water outlet and pipe membrane assemblies. It is sequentially connected with fine grating (23) and first water inlet pump (19).    USE - External anaerobic membrane bioreactor used for purifying wastewater.    ADVANTAGE - The bioreactor has low operation energy consumption, good outlet water quality, and is not difficult to be blocked.    DETAILED DESCRIPTION - External anaerobic membrane bioreactor comprises anaerobic pool (1) and several vertical pipe membrane assemblies (2) arranged in parallel and each comprises several pipe ultrafiltration membrane elements (3). The lower part of anaerobic pool is provided with water inlet (4) while its upper part is provided with water outlet (9). First water inlet pipe (10) is arranged between water outlet and pipe membrane assemblies. It is sequentially connected with fine grating (23) and first water inlet pump (19). The inlet of lower end of each pipe ultrafiltration membrane element is communicated with first water inlet pipe, while backflow pipe (11) is connected with outlet of upper end of pipe ultrafiltration membrane element. The inner diameter of pipe ultrafiltration membrane element is 5-10 mm. The pipe membrane assembly is provided with filter clean water outlet (12). The external anaerobic membrane bioreactor also comprises water inlet area (5), stuffing area (6), water outlet area (7), and methane collection area (8) sequentially arranged from bottom to top of anaerobic pool. The water inlet area is provided with sludge stirrer (32) and rotating distributor (33). The methane collection area is provided with air vent hole (21). The fine grating has filtering precision of 500-800 mu m. An INDEPENDENT CLAIM is included for wastewater purification by putting wastewater to be processed into anaerobic pool; performing anaerobic reaction while producing methane; filtering wastewater after anaerobic reaction by fine grating; and putting filtered wastewater into vertical pipe ultrafiltration membrane element at 0.5-1.0 m/s cross flow speed, such that clean water is permeated out through pipe ultrafiltration membrane element and guided out under liquid level error and gravity, while concentrated sludge left in pipe ultrafiltration membrane element flows back to anaerobic pool.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic cross-sectional view of external anaerobic membrane bioreactor.    Anaerobic pool (1)    Vertical pipe membrane assemblies (2)    Pipe ultrafiltration membrane elements (3)    Water inlet (4)    Water inlet area (5)    Stuffing area (6)    Water outlet area (7)    Methane collection area (8)    Water outlet (9)    First water inlet pipe (10)    Backflow pipe (11)    Filter clean water outlet (12)    First water inlet pump (19)    Air vent hole (21)    Fine grating (23)    Sludge stirrer (32)    Rotating distributor. (33)