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In this paper, the behavior of a new type of auxetic composite (composite with negative Poisson’s ratio) consisted of polyester fibers and ABS tubes as reinforcement as well as polyurethane foam as matrix was investigated by finite element method. Furthermore, the effect of negative Poisson’s ratio and mechanical properties of auxetic composite under quasi-static pressure were analyzed and the results were compared with the published experimental works. Good agreements were found between the results. Considering stress-strain diagram, it is concluded that this type of composite can operate as a damping material due to the specific properties such as high shear strength, indentation strength toughness. So, the foresaid properties make them a great choice with high potential application in various industries. Also, the ways to get the effective parameters to achieve more negative Poisson’s ratio were investigated. The parameters include the foam density as well as material, diameter and distances between ABS tubes. The results show that with decreasing foam density and decreasing distances between ABS tubes, the negative Poisson’s ratio increases at first to reach the critical value and then decreases.