The invention relates to a polishing machine, in particular to a plane grinding polishing machine. The plane grinding polishing machine comprises a machine platform and a mold groove formed in the machine platform, and further comprises a grinding assembly and a driving assembly of the grinding assembly; the grinding assembly comprises an oscillating shaft, an oscillating rod, a hinge shaft, a pushing rod and an eccentric disc, wherein the oscillating shaft is arranged on the machine platform in a rotating mode, one end of the oscillating rod horizontally arranged is hinged to the oscillatingshaft, the hinge shaft vertically arranged is hinged to the other end of the oscillating rod, one end of the pushing rod is hinged to the hinge shaft, and the pushing rod is connected with the eccentric disc in a rotating mode; the grinding assembly further comprises a mounting frame and a mold positioning rod, wherein the mounting frame is arranged on the oscillating rod in an erected mode, and the mold positioning rod is arranged on the mounting frame. According to the plane grinding polishing machine, fine grinding is carried out by means of rotating and oscillating back and forth at the same time, so that the grinding efficiency is effectively improved; moreover, the grinding means is moderate, and damage to a product is effectively avoided.