To explore the complex dynamics of a full-scale anaerobic filter process treating the wastewater from a purified tereplithalic acid manufacturing industry, a new modeling approach based on a moving-window-adaptive neural network is proposed. The essential feature of this modeling approach is that the neural network model is automatically updated whenever a new data block is available so that it can effectively capture the slowly changing process dynamics. To elucidate the advances of the proposed method, four different modeling approaches combined with the concepts of autoregressive with exogenous (ARX) input and a finite impulse response model were evaluated and compared. During each model identification process, a modified cross-validation technique was used to avoid the overfitting problem of a neural network. Among the tested models, a moving-window-adaptive ARX neural network model showed the best prediction ability with the smallest validation error. To investigate the feasibility of this model, various dynamic simulations were performed. Although some limitations such as ambiguity in sensitivity analysis and instability in long-term simulation were identified, it is considered that the moving-window-adaptive ARX neural network model could provide a useful guideline to explore the complicated dynamics of the anaerobic filter process.