The dielectric properties of epoxy nanocomposites with oxide-coated aluminum nanofillers were investigated at relatively low filler concentrations. The dielectric permittivities of the nanocomposites at different filler concentrations were evaluated and the optimum filler concentration was experimentally determined for two different size fillers, viz. 70 and 40 nm. Since the experiments could be conducted with only some discrete sizes and percentage of nanoparticles, an artificial neural network model was developed to predict the dielectric permittivities of the nanocomposites with different size fillers at different filler concentrations. For training the neural network model, the experimental results obtained for 70 nm nanocomposites were used. After training and validation, this model is capable of predicting the dielectric constant of the nanocomposite for any filler size at different filler concentrations. This is proved by comparing the predicted values for 40-nm composites with the corresponding experimental values. The results show that predicted values and experimental values match well at low filler concentrations. Using this model, the dielectric permittivities of the nanocomposites with fillers of varying size and concentration can be predicted.