A pulse-free pump, that employs the characteristics of a reciprocating controlled-volume type pump, enables the flow capacity to be accurately changed, and allows an extremely small volume of flow to be transported under high pressure. In addition, since the pump also has the characteristics of a diaphragm-type pump, it is possible to eliminate the problems of liquid leakage and pulsation that are inherent to reciprocating controlled-volume type pumps. Since pulsation dampers, including an accumulator, are not required, changes in flow capacity does not result in flow delays. The pump responds immediately to changes in flow capacity and provides constant flow.