Auxetic textiles have been attracted the attention of many researchers due to their enhanced mechanical behavior during loading condition. The developed Double-core helical auxetic yarn (DC-HAY) is a structural material with negative Poisson’s ratio (NPR) behavior. It consists of two similar soft yarns with a higher diameter and a stiff yarn with a lower diameter. The stiff yarn has been twisted around the soft yarns, alternatively. In this paper, the effect of structural parameters including, the initial helical angle of wrap component with five levels, diameter ratio of components with three levels, and modulus ratio of components with two levels, on Poisson’s ratio of DC-HAY, has been investigated through the full factorial experimental design method. SPSS software has been used for analyzing the results. The results showed that the highest maximum NPR belongs to the sample with the lowest initial helical angle, highest diameter ratio of components, and highest modulus ratio of components. Also, it has been found that all the main factors have a statistically significant effect on Poisson’s ratio of DC-HAY at a 95% of confidence level.