In this paper, an artificial neural network (ANN) based system-level model predictive control framework is established for a variable air volume (VAV) system to improve its robustness and energy efficiency. The VAV system consists of three processes: the zone temperature process, the damper process and the supply air volume process of the air handling unit connecting the ductwork for all of the boxes. An ANN-based predictive controller is designed for the zone temperature process, and a PI controller is used for the damper process; they operate in a cascaded manner. Another ANN predictive controller tracks the total supply air volume subject to the cooling load constraints from the lower level VAV boxes and minimizes the fan energy consumption. The ANN controllers are optimized online by the Lagrange variational approach (LVA) to minimize the system cost function and implement a feedback receding horizon optimal control. With the LVA based gradient descent training algorithm, the weight convergence of the ANN predictive controllers and stability of the control system is obtained with small computational and storage needs. The modeling methodology, based on ANNs for the above processes, is developed and calibrated with actual data measured from a site. All of the data processing and control strategy implementations are based on extensive measurements collected from a laboratory building located in the campus of Beijing University of Civil Engineering and Architecture, Beijing, China. The experimental results show that an additional 6.12% energy savings is achieved. This is accomplished by introducing the fan control signal into the system cost function as the performance index of energy consumption with a 0.2 penalty coefficient. In the presence of un-modeled disturbances and modeling errors, the framework also reduces the temperature oscillation at least by approximately 60% compared with PI control.