The present invention discloses an Up-flow Multi-stage Anaerobic Reactor (UMAR) used for treatment of medium/high concentration organic wastewater. The stated UMAR with forced internal circulation, improved phase separator and added sludge inlet overcomes the disadvantages of a lower load, a longer hydraulic retention time and a larger dimension in traditional anaerobic reactors. The forced internal circulation increases capacity and cycles of internal circulation thus increased efficiency of contaminant removal. The fast jetting is avoided and efficiency of gas/liquid separation is increased by an improved bending outlet of up flow pipe. The simplified sludge addition and usage are obtained by a sludge inlet. The load of UMAR in this invention can reach about 30 kgCOD/(m.sup.3d) for treatment of medium/high concentration of organic wastewater from pulp and paper process and similar wastewater, being about four times of load and capacity of traditional Up-flow Anaerobic Sludge Bed (UASB) reactors.