In many applications of system state forecasting, the prediction is performed using multi-dimensional data sets. The traditional methods for dealing with multi-dimensional data sets have some shortcomings, such as a lack of nonlinear correlation modeling capability (e.g., for vector autoregressive moving average (VARMA) models), and an inefficient linear correlation modeling mechanism (e.g., for generic neural fuzzy systems). To tackle these problems, an evolving fuzzy neural network (eFNN) predictor is proposed in this paper to extract representative information from multi-dimensional data sets for more accurate system state forecasting. In the proposed eFNN predictor, linear correlations among multi-dimensional data sets are captured by a VARMA filter, while nonlinear correlations of the data sets are modeled by a fuzzy network scheme, whose fuzzy rules are generated adaptively using a novel evolving algorithm. The proposed predictor possesses online learning capability and can address non-stationary properties of data sets. The effectiveness of the proposed eFNN predictor is verified by simulation tests. It is also implemented for induction motor system state prognosis. Test results show that the proposed eFNN predictor can capture the dynamic properties involved in the multi-dimensional data sets effectively, and track system characteristics accurately.