A new data-driven continuum model based on an artificial neural network is developed in this study for a new three-dimensional lattice-structured material design. The model has the capability to capture and predict the nonlinear elastic behaviour of the specific lattice-structured material in the three-dimensional continuum description after being trained through the appropriate dataset. The essential data as the input ingredients of the data-driven model are provided through a hybrid method including experimental and unit-cell level finite element simulations under comprehensive loading scenarios including uniaxial, biaxial, volumetric, and pure shear loading. Furthermore, the lattice-structured samples are also fabricated using SLA additive manufacturing technology and the experimental measurements are performed and used for validation of the model. This then illustrates that the current model/methodology is a robust and powerful numerical tool to conduct the homogenization in complex simulation cases and could be used to accelerate the analysis and optimization during the design process of new lattice-structured materials. The model could also easily be used for other engineered materials by updating the dataset and re-training the ANN model with new data.