A curved surface formation polishing apparatus for rotationally symmetrical objects such as optical lenses, mirrors, etc., which is so arranged that, by relatively displacing a processing tool (10) and a workpiece (15) in a direction generally intersecting at right angles with a rotary axis of the processing tool (10) mounted on a rotating spindle (11) so as to follow a predetermined curved surface cross section shape, grinding loci at a processing point of the workpiece formed by an abrasive grain cutting edge of the processing tool may overlap each other through crossing as the processing proceeds, thus realizing a favorable finished surface. Moreover, according to another embodiment of the present invention, since it is so arranged that, with more than two processing tools (10B1, 10B2) mounted on the same rotary axis, there is provided a device for displacing the processing tools in the direction of the rotary axis so as to change-over the processing tools according to end uses and processing steps, such change-over of the processing tools is facilitated, while it becomes possible to suppress deterioration in the accuracy of the processed shape by setting errors of the processing tools, with a simultaneous simplification of construction of the apparatus and reduction in cost for an improved mass- productivity.