Provided is a flow rate control apparatus capable of being used continuously when the apparatus is used in equipment that operates continuously, and a flow rate control method for the flow rate control apparatus. A flow rate of a fluid is controlled via any one of control valves disposed in branch passages, respectively. When replacement of the one control valve is determined to be necessary on the basis of a signal outputted from a monitoring portion of the one control valve, the one control valve performing flow rate control is closed, and another control valve disposed in another one of the branch passages, is opened, to perform flow rate control with a flow rate equivalent to that before the replacement. Furthermore, on-off valves disposed at upstream and downstream sides of the closed control valve are closed.