To attain automatic optimization of advance/retreat movement of a tailstock spindle for workpieces with different lengths.

The tailstock includes a tailstock body 30, a tailstock spindle 19, and a tailstock spindle drive means 38. A tailstock spindle position detecting means 39 is provided which consecutively detects the axial position of the tailstock spindle 19. A means 72 is provided which detects a workpiece clamp position Z3 where an end of a workpiece W supported by a main spindle 9 is supported by the tailstock spindle 19. In the workpiece clamp position detection means 72, the value obtained when the detected value of the tailstock spindle position detection means 39 has ceased to change with the tailstock spindle 19 brought near the end of the workpiece W by the tailstock spindle drive means 38 is taken as the workpiece clamp position Z3. A speed switching control means 73 is provided which conducts low-speed switching at a low-speed switching position Z2 according to the workpiece clamp position Z3.