In this study, an efficient and accurate framework based on a Graph Neural Network (GNN) is developed to predict the dielectric constants of nanomaterials, significantly reducing computational cost. The proposed model is trained on data derived from Molecular Dynamics (MD) simulations using LAMMPS and Density Functional Theory (DFT) calculations. The training dataset consists of dielectric constant values for molecular structures of TiO₂, SiO₂, H₂O, metal-organic frameworks (MOFs), graphene oxide, and carbon nanotubes under various temperature (300–500 K) and pressure (0.1 MPa–10 GPa) conditions. The GNN model achieves high prediction accuracy with a Root Mean Square Error (RMSE) of 0.12 and a Mean Absolute Error (MAE) of 0.08, while reducing prediction time to 0.5 seconds. Results show that substituting 10 copper (Cu) atoms into the TiO₂ structure enhances its dielectric constant by 20%, attributed to heterogeneous charge distribution and stronger dipole formation. Additionally, shortening the H–O bond length in water from 1.5 Å to 1.0 Å increases the dielectric constant by 15%. Sensitivity analysis and interpretability techniques such as Grad-CAM identify key structural features—including Cu and Ti atoms, bond lengths, and bond types—as critical factors influencing dielectric properties. Comparisons with traditional methods like Support Vector Machine (SVM) and linear regression confirm the superior accuracy and efficiency of the GNN model.