Ash fouling has been an important factor in reducing the heat transfer efficiency and safety of the coal-fired power plant boilers. Scientific and accurate prediction of ash fouling of heat transfer surfaces is the basis of formulating a reasonable soot blowing strategy to improve energy efficiency. This study presented a comprehensive approach of dynamic prediction of the ash fouling of heat transfer surfaces in coal-fired power plant boilers. At first, the cleanliness factor is used to reflect the fouling level of the heat transfer surfaces. Then, a dynamic model is proposed to predict ash deposits in the coal-fired boilers by combining complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and nonlinear autoregressive neural networks (NARNN). To construct a reasonable network model, the minimum information criterion and trial-and-error method are used to determine the delay orders and hidden layers. Finally, the experimental object is established on the 300 MV economizer clearness factor dataset of the power station, and the root mean square error and mean absolute percentage error of the proposed method are the smallest. In addition, the experimental results show that this multiscale prediction model is more competitive than the Elman model.