Abstract: Acid spraying has been widely applied to remove ammonia and particle matter in the exhaust gas purification at the end of intensive livestock and poultry houses. Package material can be expected to serve as the reaction site between acid solution and exhaust gas. The performance of package material can also dominate the effectiveness of exhaust gas purification in practical engineering applications. Particularly, the installation of an exhaust gas purification system is ever-increasing as the resistance of the ventilation system. The pressure drop generated by the packing material can determine whether the exhaust gas purification system can be configured. Since the porosity of packing material is often fixed, it is difficult to adjust for the different livestock and poultry houses. This study aims to fully meet the requirements of pressure drop and purification efficiency of the exhaust gas purification system in the ventilation management of livestock and poultry houses. A new structure was developed for the package material with adjustable porosity. The configuration of the base cell was also optimized in the package material, according to the lattice structure. A lattice structure was also designed with zero Poisson's ratio using a two-dimensional lattice cell optimization model, according to the topology optimization theory. The Parametric Level-set-based topology optimization was used to construct the optimization model. The optimized structure was then obtained under a randomly selected initial configuration using the iterative solution, indicating the zero Poisson's ratio. The parameterized configuration was constructed to maintain the optimized structural topology using homogeneous bars. A two-dimensional lattice was constructed to form a three-dimensional one using the periodic arrangement of the two-dimensional parameterized configuration. A systematic analysis was implemented to determine the change in porosity, pressure drop and specific surface area of the package material using numerical simulation and experiments. The test results show that the porosity of the packing material was adjusted within the range of 91.1% to 98.7% when the vertical load was changed from a tensile load of 200 N to a compressive load of −200 N. Meanwhile, the pressure drop generated by the packing material decreased from 38.0 to 4.9 Pa with the increase of porosity, while the specific surface area decreased from 16.1 to 3.9 m²/m³. Therefore, the tunable porosity was achieved in the designed lattice structure with zero Poisson's ratio under the tension and compression load in a single direction to deform. The constant size was also maintained to ensure no leakage of exhaust gas in the adjustment process. Moreover, a series of tests were carried out to clarify the influence of porosity adjustment on the purification efficiency of ammonia and particle matters PM2.5 and PM10. The test results show that the pressure drop increased from 2.7 to 35.2 Pa, while the ammonia purification efficiency increased from 77.4% to 92.6%, and the purification efficiency of PM2.5, and PM10 increased from 69.2%, and 87.2% to 90.1%, and 97.7%, respectively, when the porosity of the packaging material decreased from 98.7% to 91.1%. The pressure drop of 30 Pa was produced for the ammonia purification efficiency of 85%, and particle purification efficiency of 40% to 45%, compared with the widely-used packing material with fixed porosity of 90% in existing purification systems. The designed package material with zero Poisson's ratio can be expected for an appropriate porosity, according to the pressure drop load requirements of the ventilation system of the breeding house, and the purification efficiency fully met the requirements of ammonia removal efficiency of 83% to 90%, and particle purification efficiency should not be less than 50% for the purification of livestock and poultry house exhaust gas. In conclusion, the structure of package material can meet the porosity requirements using the pressure drop and exhaust gas purification efficiency of livestock and poultry houses. The finding can provide a theoretical basis and design reference for the automatic regulation of the porosity of package material.