The invention belongs to the technical field of slime water processing, in particular relates to a slime water classification pool based on the parabolic classification theory. The invention conducts the classification principles based on the differences in the parabolic trajectories of the coal slime particles with different shapes, weights, and sizes in the liquid medium; the pool at least comprises a pool body, an adjustable vibration board device, and a drainage mud sluggish board structure; the adjustable vibration board device comprises a vibration board, a hinge chain, flexible shock vibration pieces and an ultrasonic regulation device, and is arranged in the middle of each grading room, and the effect of speeding up the grading of coal mud particles and settlement can be achieved; the drainage mud sluggish board structure comprises an oblique board, a bracket, an axle, a bearing, and a manual rotating valve, the pool body is divided into five grading rooms and is connected with the pool bodies at the same time, the angle of the oblique board can be adjusted 360 degrees to achieve the full guidance of the coal mud particle classifications. The invention has the characteristics of being simple in structure, low in construction cost, small in maintenance workload and obvious in effect, and the like.