The usage of nanofillers in composite materials has grown over time due to various benefits, including superior properties, better adhesion, and high stiffness. To accomplish this, 150, 200, 250, and 300 gsm of hemp fiber mat with various thicknesses and weight proportions of graphene powder, including 0%, 3%, 6%, and 9%, as well as 3, 6, 18, and 25 µm-sized particles, were used. High-speed mechanical stirring was used to evenly mix the nanofiller (nanographene) with the epoxy-based nanocomposites at various loadings. We looked at the bending and interlaminar shear strength (ILSS) properties of hybrid nanomaterials. According to the study, adding 300 gsm of hemp epoxy composites filled with 6 wt% nanographene has significantly improved mechanical properties. The development of a forecasting model to determine the mechanical properties using artificial neural networks (ANN). The constructed model has a significant connection with the test findings. A correlation of 0.9724 for the Levenberg–Marquardt training procedure indicates a significant connection between the predicted and experimental artificial neural models. The observational and projected results for bending and ILSS have <3% and 4% errors, corresponding to the ANN prediction and Taguchi L16 matrix. The potential of ANN for forecasting the bending and ILSS of composite materials is expanded by the close relationship between ANN and experimental findings. The following parameters were used in the current study to determine the flexural strength: graphene content (40.79%), graphene size (34.19%), the number of hemp layers (12.57%), and hemp fiber thickness (11.65%). Similar to ILSS, graphene content accounts for 47.82% of the total, with graphene size (27.87%), hemp fiber thickness (11.80%), and the number of hemp layers (also 11.80%) all contributing (11.78%).