To prevent increase of a flow rate of medicine caused by relative pressure fall by arranging a pressure controlling means which monitors pressure along a main flow passage at a position upstream from a primary flow rate controlling part, and a governing means for fluid flow from a storing part of the medicine to a patient in response to fluctuation of the monitored pressure.

A flow rate controlling pump 12 is composed of a valve housing 32 having an elastic diaphragm 34 which divides the valve housing 32 into a pressure controlling chamber 36 and a flow chamber 38. The pressure controlling chamber 36 is filled with gas of specified pressure. The flow chamber 38 is serially connected to a main flow passage 24 on a downstream side of a primaly flow rate controlling part or a minute pipe 26 through an inlet valve port 40 having an elastic valve seat 42. During a normal operation state, that is, in the case that environmental pressure is higher than the pressure inside the pressure controlling chamber 36, the diaphragm 34 is separated from the valve seat 42. Medicine flowed through the flow chamber 38 and an outlet port 44 from the valve port 40. Encountering low environmental pressure, the diaphragm 34 responds to the pressure difference and is operated for closing the valve seat 42.