The present invention is an improved flow-metered pumping system using an air-backed diaphragm pump with load compensation. A variable motor speed controller is used to compensate for flow rate reduction caused by pressure effects. When the output pressure on the pump increases to a point where the load on the pump motor exceeds a specified threshold, the motor speed controller increases the speed of the motor to compensate for pressure induced diaphragm distortion losses and to achieve a substantially constant flow rate across a range of pump output pressures.