In this work, a new structure for designing auxetic yarn and its geometrical analysis is presented. The proposed structure is referred to as a double-core helical auxetic yarn (DC-HAY). It consists of two core components of soft yarn with a larger diameter and one wrap component of stiff yarn with a smaller diameter. A primary geometrical model for predicting the Poisson's ratio of the structure was presented through the deformation analysis of the DC-HAY during the tensile loading. Also, the primary proposed model was modified by considering the non-linear behavior of Poisson's ratio of the core components. For the verification of the proposed models, some experiments were conducted based on the initial wrapping angle, as well as the diameter ratio and modulus ratio of components. The results showed that the proposed yarn structure exhibits an apparent auxetic outcome. Moreover, the modified model is capable of predicting the maximum negative Poisson's ratio of the DC-HAY with a desirable error. Furthermore, it was found that the higher modulus ratio of components, higher diameter ratio of components and the lower initial wrapping angle will result in a higher maximum NPR, which were −8.23, −8.16 through the main lateral directions of samples.