This paper describes a method for robots to perform appropriate cutting operations on curved vegetables according to their shape. Although there are many studies on robots cutting vegetables, these studies do not deal with curved vegetables. In this study, the robot’s cutting motion is made to follow the center line of the curved vegetable. This method uses a modeling based on a center line and three parameters to realize cutting curved vegetables into round slices, diagonal slices, and large chunks. Cutting into large chunks is performed by changing the direction of the knife instead of turning the vegetable. This method was implemented on a dual-armed robot and experiments were conducted to cut cucumbers, eggplants, and bananas. As a result, it was confirmed that even curved vegetables could be cut.