A machining apparatus for improving the roundness of a work. The outer circumference of a work is divided into predetermined intervals, and a difference between the radius of that portion of the work which has finished being machined and a target radius thereof is detected for each of the intervals mentioned above. The position of a tool which corresponds to every predetermined angle of rotation thereof is corrected on the basis of a detected radius difference at each of the intervals. The path of the tool is interpolation-computed on the basis of these corrected positions. The tool is turned along the path thus interpolation-computed, so that the work is machined with a high precision.