Honeycomb structures are widely utilized across various fields. Chiral honeycombs are recognized for their superior energy absorption capabilities, and curved-wall honeycomb cells are known to mitigate stress concentration issues. The energy absorption properties of curved four-chiral honeycomb structures and the data-driven design approach for these structures were proposed. A finite element model of a tetra-chiral honeycomb structure was established, and its results were compared with those obtained from compression experiments conducted on 3D-printed models. Consistency between the two sets of results was observed, thereby verifying the reliability of the finite element model. Subsequently, a multi-input multi-output artificial neural network model was constructed based on a large number of finite element models. The input variables for this model, which included the transverse and longitudinal angles of the honeycomb cells and the wall thickness, were processed to predict output variables such as peak force, plateau stress, and energy absorption capacity. It is found that prediction errors are maintained within 7%, indicating that the neural network model demonstrates excellent predictive performance. Furthermore, an inverse design network is developed to design optimal structures based on specified energy absorption characteristics. Results show that the inverse neural network achieves high prediction accuracy for both the transverse and longitudinal angles of the cells and the wall thickness. The findings of this study provide theoretical guidance for the engineering applications of such honeycomb structures.