A vessel of a liquid pressure generating apparatus is divided into two vessels of an upper liquid pressure generating vessel containing therein a liquid chamber whose volume can be varied, and a lower medium vessel into which is filled a medium which varies between a gaseous state and a liquid state. Both the vessels are connected by a communicating passage. The two vessels are respectively provided with heating heat exchange portions into which is inputted an external heat such as a waste heat of a driving source of a vehicle. The medium vessel is also provided with a cooling heat exchange portion. By the inputting of heat and stopping thereof, the liquid pressure can be controlled with good response.