To establish a high speed operation without increasing the pumping capacity of a hydraulic unit.

A moving element driving device concerned is composed of a cylinder 3 to drive a tail stock 2, etc., an oil pressure source 6 supplying thereto an oil pressure via the first path, and a second path 9 connected parallel to the first path 8. The second path 9 is equipped with an oil quantity increasing means 10 such as a booster to make the oil flow-out quantity greater than the flow-in quantity. A path selecting means 16 puts the first path 8 and second path 9 in communication with the cylinder 3 selectively.