Hierarchical metamaterials with particularly designed microstructure may exhibit unconventional mechanical properties, such as chiral effects, negative Poisson’s ratio (NPR) or negative thermal expansion coefficient (NTEC). Due to the internal rotational degrees of freedom at each material point in chiral materials, uniaxial-torsion or uniaxial bending deformation couplings may occur, as predicted by the non-centrosymmetric Cosserat elasticity or strain gradient elasticity. Such couplings are of great importance for novel sensor technologies. In this work, deep neural networks (DNN) are developed to learn the responses of hierarchical metamaterials with desired chiral microstructures for their NPR, NTEC and coupling effects. The geometric data of chiral microstructures are provided, along with effective mechanical properties calculated from finite element analysis, as well as experimental data, to train the DNN model. Experimental specimens are manufactured from 3D printing techniques. Furthermore, the geometries of hierarchical metamaterial design are generated from a generative adversarial neural network for enhanced effective mechanical properties, such as NPR.