A throwaway insert for a ball end mill having an ideal cutting edge shape corresponding to the cutting speeds and loads at different portions of the cutting edges, high in strength and capable of discharging chips smoothly. As viewed in a direction perpendicular to the line connecting noses, each cutting edge forms a convex curve with its nose portion at the lowest level. As viewed in a direction perpendicular to the abovesaid direction, rake faces form symmetrical, downwardly sloping convex accurate surfaces or straight surfaces having a positive rake angle of 5-25.degree.. The wedge angle at the cutting edges is set at 85-65.degree.. Thus, the rake angle will be negative at the noses and positive at other portions. Further, the rake angle increases toward the side where the cutting speed is higher. The thickness of the insert increases toward the side where the load is greater. Since this insert is a modification of a negative insert, i.e. an insert of the type having a side perpendicular to its bottom, it has enough strength. Chips can be discharged smoothly too.