Stent migration is one of the common complications after tracheal stent implantation. The causes of stent migration include size mismatch between the stent and the trachea, physiological movement of the trachea, and so on. In order to solve the above problems, this study designed a non-uniform Poisson ratio tracheal stent by combining the size and structure of the trachea and the physiological movement of the trachea to improve the migration of the stent, meanwhile ensuring the support of the stent. In this study, the stent corresponding to cartilage was constructed with negative Poisson's ratio, and the stent corresponding to the circular connective tissue and muscular membrane was constructed with positive Poisson's ratio. And four kinds of non-uniform Poisson's ratio tracheal stents with different link lengths and negative Poisson's ratio were designed. Then, this paper numerically simulated the expansion and rebound process of the stent after implantation to observe the support of the stent, and further simulated the stretch movement of the trachea to calculate the diameter changes of the stent corresponding to different negative Poisson's ratio structures. The axial migration of the stent was recorded by applying different respiratory pressure to the wall of the tracheal wall to evaluate whether the stent has anti-migration effect. The research results show that the non-uniform Poisson ratio stent with connecting rod length of 3 mm has the largest diameter expansion in the negative Poisson ratio section when the trachea was stretched. Compared with the positive Poisson's ratio structure, the axial migration during vigorous breathing was reduced from 0.024 mm to 0.012 mm. The negative Poisson's ratio structure of the non-uniform Poisson's ratio stent designed in this study did not fail in the tracheal expansion effect. Compared with the traditional stent, the non-uniform Poisson's ratio tracheal stent has an anti-migration effect under the normal movement of the trachea while ensuring the support force of the stent.