The invention relates to a full-automatic multi-grinding head independently moving polishing machine, which comprises a controller, a main motor, a cleaning device and a conveyer belt. A grinding head and a stand are fixedly connected with an upright post respectively, the top of the upright post is fixedly connected with an upper beam, and the grinding head is connected with a main shaft of a main shaft box. The polishing machine is characterized in that the main motor drives the main shaft of the main shaft box through a first-level conveyer belt, the main shaft is connected with the grinding head, the main shaft box is respectively connected with an independent left moving mechanism and an independent right moving mechanism as well as a lifting mechanism, and the lifting mechanism comprises a mechanical lifting mechanism and a pneumatic lifting mechanism. The polishing machine has a compact and reasonable structure, a single grinding head can swing solely, and the single grinding head can solely grind an irregular plate with an unfilled corner, so that the polishing machine radically solves a fundamental problem for stabilizing yield and quality. The polishing machine adopts pneumatic and mechanical double-level lifting so as to increase lifting stroke, and is widely applied for machining stones, so that the polishing machine not only can grind the prior stones, but also can grind various boulder strips with different heights and specifications. The polishing machine has the advantages of high working efficiency and long service life.