This paper proposes an intelligent forecasting system based on a feedforward neural network aided grey model (FNAGM), integrating a first-order single variable grey model (GM(1,1)) and a feedforward neural network. The system includes three phases: initialization phase, GM(1,1) prediction phase, and FNAGM prediction phase. A number of parameters required for the FNAGM are selected in the initialization phase. A one-step ahead predictive value is generated in the GM(1,1) prediction phase, followed by the implementation of a feedforward neural network used to determine the prediction error of the GM(1,1) and compensate for it in the FNAGM prediction phase. We also adopted on-line batch training to adjust the network according to the Levenberg-Marquardt algorithm in real-time. According to the experimental results of a robot, the proposed intelligent forecasting system can provide high accuracy for both trajectory prediction and target tracking.