A novel type of tubular structure with negative Poisson's ratio based on gyroid-type triply periodic minimal surfaces (TPMSs) is proposed in this study. This work is an attempt to design auxetic tubular structures based on TPMS. A series of auxetic tubular structures were designed and then fabricated using laser power bed fusion. Compressive behaviours of the fabricated auxetic tubular structures were investigated using experimental and numerical methods. To obtain optimal designs of tubular structures with controllable auxetic properties, the influence of several parameters were investigated comprehensively. Subsequently, several graded auxetic tubular structures were designed based on the parametric analysis and studied numerically. The mechanical properties of the tubular structures could be controlled effectively using the proposed approach. The proposed method can be used for guiding the design and optimisation of auxetic tubular structures, showing excellent potential for various applications such as biomedical devices, vehicle crashworthiness, and protective engineering.