Cellular mechanical metamaterials are a special class of materials, whose mechanical properties are primarily determined by their geometry. But capturing the nonlinear mechanical behavior of these materials, especially with complex geometries and under large deformation can be challenging due to the inherent computational complexity. In this work, we propose a data-driven multiscale computational scheme to as a possible route to resolve this challenge. We use a neural network to approximate the effective strain energy density as a function of cellular geometry and overall deformation. The network is constructed by “learning” from the data generated by finite element calculation of a set of representative volume elements at cellular scales. This effective strain energy density is then used to predict the mechanical responses of cellular materials atlarger scales. Compared with direct finite element simulation, the proposed scheme can reduce the computational time up to two orders of magnitude. Potentially, this scheme can facilitate new optimization algorithms for designing cellular materials of highly specific mechanical properties.