Abstract: An apparatus for finishing the edge of a sheet of glass, which includes a supporting structure with a support base, a stationary vertical structure coupled on the support base, and, an upper supporting arm located in a horizontal position on the vertical stationary structure. A motor is connected at one end of the upper supporting arm. Grinding means are connected to the motor fort finishing or grinding the edge of sheet of glass. A housing for housing the grinding means, which includes a fixed upper section and a removable lower section. A longitudinal groove is made in the housing for the introduction of the edge of the glass sheet to contact with the grinding means in order to finish the edge of the glass sheet. Cooling means are located within the housing for cooling the periphery, lower and upper sections of the grinding means during the finishing of the edge of the glass sheet.