The invention discloses a two-phase tow-period anaerobic organism reactor processing wastewater. The reactor comprises a reactor body, a circulation tank, an alkali adding device, a biological phase separator, a primary three-phase separator and a secondary three-phase separator, wherein the circulation water tank and the alkali adding device are arranged on the outer side of the reactor body, and the biological phase separator, the primary three-phase separator and the secondary three-phase separator are arranged in the reactor body from bottom to top, a closed acidification reaction chamberis arranged at the lower part of the reactor body, and the biological phase separator is arranged at the top in the acidification reaction chamber; a methane-generating main reaction area is formed between the upper part of the acidification reaction chamber and the primary three-phase separator, and a methane-generating fine processing area is formed between the primary three-phase separator andthe secondary three-phase separator. The anaerobic organism reactor provided by the invention has the advantages that the structure is compact, the occupying area is small, the organic load reaches to 40kg COD (chemical oxygen demand)/(m<3>.d) when the reactor is used for processing high-concentration wastewater generated by pulping and paper making or similar wastewater, and the stability and the flexibility are extremely high when the reactor is used for processing wastewater with variable water quantity and water quality.