A fluid infusion device and a method of using the same. The device includes an outer, flexible guide catheter having a distal end for introduction beneath the skull of a patient and a proximal end remaining external of the patient. A flexible infusion fiber is located within the guide catheter and has a distal end extending outwardly from the guide catheter to be located in a target area within the patients brain. The infusion fiber can be fixed or axially movable within the guide catheter. In the latter embodiment, the proximal end of the infusion fiber extending outwardly from the guide catheter can be manipulated to locate the distal end of the infusion fiber in the target area. An infusion pump is connected to the proximal end of the infusion fiber to infuse a minute quantity of fluid at an extremely low flow rate into the brain of the patient.