Disclosed is a pneumatically powered high-pressure and lightweight fluid pump. The pump is useful for pumping fuel for liquid rocket engines and for transferring liquids from one space vehicle to another. During operation of the pump, liquid is drained from a tank into a pump chamber and the chamber is then pressurized to deliver fluid. The chamber is then refilled from the main tank. An auxiliary chamber supplies fuel while the main chamber is being filled, thereby a steady stream is delivered from the pump. The auxiliary chamber is refilled from the tank while the main chamber is delivering fluid. In order to transfer fluid from the tank to the pump chamber, the pressure in the pump chamber is maintained at a pressure higher than the vapor pressure of the fluid being pumped but lower than the pressure in the tank.