Disclosed is a multi-stage sedimentation rake-free thickening device. The device includes a central tank. A diversion sedimentation zone is arranged on the outside of the center tank. The diversion sedimentation zone includes an annular diversion sedimentation screen and a concentrated magnetic shower. The annular diversion sedimentation screen includes an annular groove spirally arranged around a central groove body. The annular groove is sequentially arranged with second spoiler baffles along the length direction. The lower bottom plate of the annular groove is also provided with second underflow discharge port. Multiple second inclined plate diversion discharge pipe is arranged under the corresponding second underflow discharge ports. The outlets of all the second inclined plate guide discharge pipes are collected to the second underflow discharge pipe, and the settled water is discharged from the second overflow discharge pipe arranged at the end of the annular groove.