To provide a curling working apparatus and a curling working method having a wide application range where not only a can with a circular cross-section but also a can with a noncircular cross-section can be treated.

In the curling working apparatus1, the rim of a can C is curled by a roller-shaped curling tool 40 having a concaved working face. A two-dimensional moving apparatus 20 supports the can C, and a pivot supporting apparatus 30 supports the curling tool 40. An X-axis servomotor 22 and a Y-axis servomotor 23 perform the moving control of the two-dimensional moving apparatus 20 so that one place of the rim of the can C is contacted with the curling tool 40. In the contact place between the rim of the can C and the curling tool 40, a θ-axis servomotor 37 performs the control of the angle of the pivot supporting apparatus 30 so that the rotation axis of the curling tool 40 orients to the center of the curvature of the can C in the contact place. A Z-axis servomotor 34 controls the relative distance in a vertical direction between the two-dimensional moving apparatus 20 and the pivot supporting apparatus 30.