To provide such a hydraulic driver for a running vehicle mounted with a working machine as being capable of showing the maximum tractive force to the extent that wheels do not easily slip with the stepping of a fuel pedal, even if forwarding load work such as stubbing work for a bucket into sediment blocks is done on an easy-to-slip or easy-to-collapse ground.

A differential pressure adjusting circuit 21 which is formed with an electromagnetic opening/closing valve 22, a throttle 23 and a relief valve in a series circuit is provided in parallel to a throttle 5 at the downstream side of a charge pump 4. When forwarding load work is done, a switch 25 is closed to open the electromagnetic open/closed valve 22 and open the relief valve 24 when the rotating number of a motor 1 is somewhat increased, so that pilot oil can flow through the throttle 23. In this way, the throttle 5 which adjusts the tilting of a variable capacity hydraulic pump 2 via a link 17 displaced with the switching operation of a switching cylinder 12 is less varied up and down in differential pressure.