The implementation of a machine learning approach to predict vibration suppression, as derived from nanocomposite laminates with piezoelectric shunted systems, is studied in this article. Datasets providing the vibration response and vibration attenuation are developed using parametric finite element simulations. A graphene/fibre-reinforced laminate cantilever beam is used in those simulations. Parameters, including the graphene and fibre reinforcements content, as well as the fibre angles, are among the inputs. Output is the vibration suppression achieved by the piezoelectric shunted system. Artificial Neural Networks are trained and tested using the derived datasets. The proposed methodology can be used for a fast and accurate prediction of the vibration response of nanocomposite laminates.