Disclosed is an automatic constant pressure polishing apparatus. The automatic constant pressure polishing apparatus comprises a housing having a hollow section therein, a rubber pad installed in the housing and having superior expansion and contraction characteristics, a pressure fixture having a male screw section, which is formed on an outer peripheral surface thereof in order to press and fix the rubber pad, and a central hole formed at a central portion thereof, a slider screw-coupled into the housing to adjust pressure in the housing according to a rotational degree of the rotating shaft, and a polishing pad installed at a front end portion of the housing.