Purpose Fused filament fabrication (FFF) is a widely used 3D printing technique for the fabrication of mechanical metamaterials with intricate geometries. Gradient strategy is applied to geometric parameters of gradient star re-entrant hybrid auxetic (GSRA) structure. Deformation behaviour is studied under compressive loading. The purpose of this study is to investigate the influence of gradient geometric parameters on mechanical properties, namely, specific strength (SS), specific modulus (SM) and specific energy absorption (SEA). Design/methodology/approach Response surface methodology (RSM) is implemented for the design of experiments of gradient geometric parameters to minimize the number of experimental tests. Acrylonitrile butadiene styrene material is used for the fabrication of GSRA structures by FFF technique. The best set of gradient parameters has been optimized maximizing all three responses using RSM and artificial neural network optimization technique. Findings During compressive testing, row-wise deformation is observed with two-stage plateau regions, which results in increase in SEA of the structure. Furthermore, based on analysis of variance and 3D response plots, it is found that height gradient is the most influencing gradient geometric parameter on SS and SM, whereas the wall thickness gradient has maximum influence on SEA. Meanwhile, the interaction effect of wall thickness gradient and height gradient has maximum influence on SS, SM and SEA. Research limitations/implications This study of applying gradient strategy to geometric parameters is limited to GSRA structure under compressive loading. In addition, findings are valid within the selected range of gradient geometric parameters. These findings are useful for the selection of gradient geometric parameters to maximize SS, SM and SEA of GSRA structure simultaneously. These outcomes pave the way for designing light-weight gradient hybrid auxetic structures in the field of construction, aerospace, automobile and biomedical engineering. Originality/value Limited experimental study is available on investigating the influence of gradient geometric parameters on mechanical properties, namely, SS, SM and SEA, and deformation behaviours of hybrid auxetic structures. This study directly addresses the above research gaps.