A variable-speed magnetic coupling having a radially movable magnet, comprising a drive disc assembly (I), a driven disc assembly (II), and a speed adjusting device assembly (III). Relative rotation of a speed adjustment sleeve (15) with respect to a drive shaft (16) is achieved by means of contact and fitting of a cylindrical pin (20) with respect to a vertical recess on an inner wall of the drive shaft and to an inclined recess on an inner wall of the speed adjustment sleeve. The speed adjustment sleeve is connected to a circular slotted disc (18) by means of a screw. A permanent magnet (10) is attached to a permanent magnet bearer (9) and inserted into a rectangular through hole of a circular frame (13), and a radial movement of the permanent magnet is enabled by means of a cam and groove sliding block mechanism consisting of the circular slotted disc, the circular frame, the permanent magnet bearer, and the permanent magnet. By moving a movement block (21) to drive the movement pin (20) to slide in the recesses of the drive shaft and the speed adjustment sleeve and then drive the speed adjustment sleeve to rotate, the present invention enables a radial movement of the permanent magnet, and then changes a coupling area or an air gap distance between the permanent magnet and conductive rings (8, 11) on two sides, thus changing a magnetic flux density of the air gap, and accordingly enabling speed adjustment.