Method of continuous preparation of reclaimed rubber using multi-stage screw extruders, comprising: first, mixing waste rubber powder and softener in a mixer for 5 to 25 minutes at 60°C to 120°C to obtain a mixture, then the mixture being transported into a thermal insulation buffer tank kept at 60°C ~ 120°C, and fed into a first counter rotating twin screw extruder through a thermal insulation conveying and metering apparatus, wherein the mixture stays for 1 to 6 minutes at 100°C to 340°C in the extruder to complete uniform penetration of the softener into the waste rubber powder and preliminary devulcanization, cooling the mixture to 40 to 80°C under airtight conditions in a continuous cooling apparatus to obtain a preliminary devulcanized material with Mooney viscosity of 100 to 230, adding the preliminary devulcanized material continuously into a second multi screw extruder, adding a devulcanizing agent through a side feeding apparatus and controlling the temperature of a barrel and mandrel of the multi screw extruder at 20 to 110°C, proceeding devulcanization reaction for 1 to 6 minutes to obtain devulcanized rubber powder with Mooney viscosity of 70~150 and extruding the devulcanized rubber powder, cooling the devulcanized rubber powder to 25°C to 60°C under airtight condition in a continuous cooling apparatus, continuously adding the devulcanized rubber powder into a third multi screw extruder, controlling the temperature of barrel and mandrel of the multi screw extruder at -5 to 50°C and refine the devulcanized rubber powder for 1 to 10 minutes under shear condition, wherein refining process is finished as the reclaimed rubber is extruded from the third extruder and passes a molding apparatus and a cooling apparatus to cool to below 50°C, the required reclaimed rubber is obtained after package; wherein the mass ratio between waste rubber powder, softener and devulcanizing agent is 100:(2 ~ 20): (0.01 ~ 3); softener is one of coal tar, aromatic hydrocarbon oil, pine tar, tall oil, dipentene, paraffin oil, oleic acid, cottonseed oil, rosin, or combinations thereof; said devulcanizing agent is one of an aromatic hydrocarbon disulfide, a multi alkyl phenol sulfide, a phenyl mercaptan, an amine compound, or combinations thereof; waster rubber powder is one of waste radial truck tire powder, waste passenger car tire powder, or combinations thereof. wherein the mixture stays for 1 to 6 minutes at 100°C to 340°C in the extruder to complete uniform penetration of the softener into the waste rubber powder and preliminary devulcanization, cooling the mixture to 40 to 80°C under airtight conditions in a continuous cooling apparatus to obtain a preliminary devulcanized material with Mooney viscosity of 100 to 230, adding the preliminary devulcanized material continuously into a second multi screw extruder, adding a devulcanizing agent through a side feeding apparatus and controlling the temperature of a barrel and mandrel of the multi screw extruder at 20 to 110°C, proceeding devulcanization reaction for 1 to 6 minutes to obtain devulcanized rubber powder with Mooney viscosity of 70~150 and extruding the devulcanized rubber powder, cooling the devulcanized rubber powder to 25°C to 60°C under airtight condition in a continuous cooling apparatus, continuously adding the devulcanized rubber powder into a third multi screw extruder, controlling the temperature of barrel and mandrel of the multi screw extruder at -5 to 50°C and refine the devulcanized rubber powder for 1 to 10 minutes under shear condition, wherein refining process is finished as the reclaimed rubber is extruded from the third extruder and passes a molding apparatus and a cooling apparatus to cool to below 50°C, the required reclaimed rubber is obtained after package; wherein the mass ratio between waste rubber powder, softener and devulcanizing agent is 100:(2 ~ 20): (0.01 ~ 3); softener is one of coal tar, aromatic hydrocarbon oil, pine tar, tall oil, dipentene, paraffin oil, oleic acid, cottonseed oil, rosin, or combinations thereof; said devulcanizing agent is one of an aromatic hydrocarbon disulfide, a multi alkyl phenol sulfide, a phenyl mercaptan, an amine compound, or combinations thereof; waster rubber powder is one of waste radial truck tire powder, waste passenger car tire powder, or combinations thereof.