A cooling apparatus includes a lubricating fluid tank, a lubricating fluid nozzle, a lubricating fluid regulating device, a cooling fluid tank, a cooling fluid nozzle and a cooling fluid regulating device. The cooling fluid nozzle supplies cooling fluid to the workpiece to enhance cooling effect of the cooling fluid. The lubricating fluid nozzle feeds lubricating fluid to the machining zone to prevent frictional heat generated in the machining zone from raising temperature of the workpiece. Since an appropriate amount of the lubricating fluid within the range helps the cooling effect of the cooling fluid, a quantity of the cooling fluid is reduced within the minimum range of the cooling fluid. A consumption of the lubricating fluid is much smaller than that of the cooling fluid. Therefore, a total amount of the fluids is extremely reduced. The range of flow rates of the lubricating fluid has an upper limit that is preferably approximately 100.0 cm3/h or smaller in 1.0 mm of a contacting length in the machining zone. The range of flow rates of the cooling fluid has an upper limit that is preferably approximately 500.0 cm3/min or smaller in 1.0 mm of a contacting length in the machining zone.