A grinding and polishing machining method capable of achieving infinitely variable speeds includes the following steps that firstly, a rectangular thin sheet sample after linear cutting adheres to thelower surface of a workpiece disk in the circumferential direction; secondly, an upper grinding device is fixed to the table face of a lower grinding device; thirdly, the workpiece disk is made to reach an assigned position in the Y direction, and achieves the fixed eccentric distance with a grinding disk, a grinding disk driving motor is started, and the grinding disk is made to work; and fourthly, when machining starts, grinding liquid is added to the surface of the grinding disk provided with a groove, a driving motor of the workpiece disk is started, the workpiece disk is made to rotate,driving of the workpiece disk is achieved by the workpiece disk driving motor through a stepless variable speed mechanism, the workpiece disk driving motor is connected with the large end shaft diameter of a conical rolling wheel of the stepless variable speed mechanism through a coupler belt, and the conical rolling wheel is driven to rotate; and the grinding liquid is added into the surface of the grinding disk regularly in the grinding process. The grinding and polishing machining method capable of achieving the infinitely variable speeds achieves the function requirement that speed is anyand adjustable in a certain range, and the speed requirement in actual is guaranteed.