A hierarchical multiscale off-road mobility model is enhanced through the development of an artificial neural network (ANN) surrogate model that captures the complex material behavior of deformable terrain. By exploiting the learning capability of neural networks, the incremental stress and strain relationship of granular terrain is predicted by the ANN representative volume elements (RVE) at various states of the stress and strain. A systematic training procedure for ANN RVEs is developed with a virtual tire test rig model for producing training data from the discrete-element (DE) RVEs without relying on computationally intensive full vehicle simulations on deformable terrain. The ANN surrogate RVEs are then integrated into the hierarchical multiscale computational framework as a lower-scale model with the scalable parallel computing capability, while the macroscale terrain deformation is described by the finite element (FE) approach. It is demonstrated with several numerical examples that off-road vehicle mobility performances predicted by the proposed FE-ANN multiscale terrain model are in good agreement with those of the FE-DE multiscale model while achieving a substantial computational time reduction. The accuracy and robustness of the ANN RVE for fine-grain sand terrain are discussed for scenarios not considered in training datasets. Furthermore, a drawbar pull test simulation is presented with the ANN RVE developed with data in the cornering scenario and validated against the full-scale vehicle test data. The numerical results confirm the predictive ability of the FE-ANN multiscale terrain model for off-road mobility simulations.