In this paper, a neuro-adaptive PI control strategy for a water-cooled centrifugal chiller system is developed, and its control performance is examined. The system model consists of a flooded evaporator, a flooded condenser, a centrifugal compressor, and an electronic expansion valve. The overall system consists of three control loops: a compressor speed control loop, an inlet guide vane (IGV) control loop, and a condenser liquid level control loop. A neuro-adaptive control strategy for compressor speed control was designed. The control performance of the chiller was tested by carrying out simulation runs using an integrated building and HVAC (IB-HVAC) system model. The major details of the IB-HVAC model are described in this paper. Results show that the neuro-adaptive controller can adapt to new system dynamics of the IB-HVAC system and give good setpoint tracking responses under a wide range of operating conditions. The results show that the neuro-adaptive controller performs better than the constant gain PI controller in terms of speed of response and setpoint tracking properties.