The invention relates to a desanding and descaling device in a landfill leachate anaerobic treatment system, and an implementation method thereof. An inflow water guiding part is connected with a water inlet tube section provided with a hydraulic sand washing mixer; a sand-water separation part is provided with a cyclone paddle stirrer; an effluent water collecting part is provided with a triangular effluent water weir and an annular effluent water collecting tank; and a sand scale discharge part is provided with a screw press conveyor and a sand-water separation discharge tube. Water flow enters a circular barrel and a conical barrel for hydrocyclone desanding, and sand scales settle, and gather in a sand scale collecting hopper under the action of the cyclone paddle stirrer. The water flow flows upwards through a flow guide inclined plate or inclined tube, and ascending effluent water is collected and then is discharged out of the system through a clear liquid outlet tube. The sand scales are conveyed, lifted, pressed and dehydrated through the screw press conveyor, and fine sands and scale blocks are discharged out of the system. The device integrates sand washing, sand settingand sand-water separation functions, and realizes non-shutdown emptying and high-efficiency stable running of the leachate anaerobic treatment system.