In a scroll fluid machine, a driving shaft has an eccentric axial portion around which an orbiting scroll revolves while the orbiting scroll engages with a fixed scroll. A cooling path extends through the driving shaft to a gap between the outer circumferential surface of the eccentric axial portion and the inner circumferential surface of an axial hole of the orbiting scroll. A cooling gas is introduced into the cooling path to cool bearings around the driving shaft. A forced convection generating portion is provided on the driving shaft for sucking the cooling gas into the gap and discharging the gas.