A turret machine tool has a slide table mounted on a machine base for movement toward and away from a workpiece to be machined. A turret head is indexably mounted on the slide table, and a plurality of multispindle heads mounted on the turret head at spaced angular intervals in an indexing direction of the turret head, each of the multispindle heads having a plurality of spindles disposed therein. A plurality of machine tools mounted on respective ends of the spindles, and a plurality of spindle gears are mounted on the spindles, respectively. A driven gear is mounted in each of the multispindle heads in mesh with the spindle gears through a train of gears. A drive gear is axially movably disposed in the turret head for movement into and out of mesh with the driven gear in one of the multispindle heads which has been indexed. A plurality of gear shafts are supported in a cantilevered fashion by each of the multispindle heads and project toward the turret head, the train of gears and the driven gear being mounted on the gear shafts. The multispindle heads can be highly accurately installed on the turret head, and the train of gears can easily be serviced. The turret machine tool is relatively light in weight, and can be manufactured relatively inexpensively.