PURPOSE: To cut the paraboloid of revolution with high accuracy, by rolling the work side in accordance with the rotary angle of a single point cutting tool such that the edge of the cutting tool will draw the parabolic curve on the work cutting face.

CONSTITUTION: In the pulse trains of the simultaneous two axis produced from a numeric controller 30, one is provided to a rotary motor 14 to rotate a tool shaft 16 while the other is provided to a servo motor 26 to rotate a work supporter 20 thus to control such that the edge of the cutting tool 15 will draw the parabolic curce on the cutting face of the work and the rotate a rotary table 21 with low speed thus to cut the rotary parabolic face while satisfying the condition shown on the drawing. Here (a) is the focus distance of the paraboloid of revolution, (d) is the diameter of revolution of the cutting tool 18, P is the distance between the center of rotation of the cutting tool 18 and the center of rolling, θ is the rotary angle of the cutting tool and Θ is the rolling angle.