One of the major challenges in pharmaceutical chemistry is the accurate prediction of molecular electronic properties that influence drug behavior. The HOMO-LUMO energy gap, as a key descriptor of chemical reactivity and stability, plays a crucial role in both pharmacodynamic and pharmacokinetic properties. Although methods such as Density Functional Theory (DFT) are highly accurate, their high computational cost makes them unsuitable for large-scale screening. In this study, a machine learning-based model was developed to rapidly predict this energy gap. A dataset of 8,676 cata-condensed polyaromatic compounds containing 3 to 10 fused benzene rings was compiled. Nine chemically meaningful features were extracted and used to train multilayer perceptron (MLP) and recurrent neural network (RNN) models. The best-performing MLP model achieved an R² score of 0.9750 and a test loss of 0.0037. Saliency map analysis revealed that features such as ionization potential, electron affinity, and total energy had the most significant impact. These findings demonstrate that AI-based models can not only achieve high predictive accuracy but also provide valuable insights for drug design.