A flexible power transmission device comprises an input shaft, a conductor cylinder, conductor rings, a permanent magnet cylinder, permanent magnets, an output shaft, a spline and a spline hub, wherein the conductor rings are mounted on the inner wall of the conductor cylinder; the permanent magnets are mounted on the outer wall of the permanent magnet cylinder; an air gap is formed between each permanent magnet and each conductor ring; the permanent magnet cylinder is connected with the output shaft; the spline is connected with the input shaft; the spline hub is connected with the conductor cylinder; and the spline is connected with the spline hub. Compared with the prior art, the device synchronously rotates with other parts, and the conductor cylinder is driven to regulate the flexible power transmission, so that dynamic load interference caused by change of speed difference during regulating of a load device is reduced, and the regulation becomes simple, stable and efficient.