To machine an axis-asymmetric curved surface with high accuracy without being limited by the interference with a workpiece even when the axis-asymmetric curved surface has a large depth and a small curvature.

In cutting a curved surface, the surface of the workpiece 3 is machined by means of a cutting tool 9 into the curved surface by moving the cutting tool 9 relative to the workpiece 3, the cutting tool 9 having a doughnut shape turning locus of the cutting edge. The surface of the workpiece 3 is machined in the state that a rotary spindle 7 for holding and turning the cutting tool 9 is tilted by a specified angle θ with respect to a workpiece holding surface 3a for holding the workpiece 3. In cutting the workpiece 3, the following two processes are repeated, a process for advancing and receding the workpiece 3 toward the cutting tool 9 so as to give a required shape while feeding the cutting tool 9 in the first direction along a holding surface 3a, and a process for feeding the cutting tool 9 in the second direction perpendicular to the first direction.