Nylon cord rubber has the advantages of small residual deformation and is easy to lift and lower the tubing string in low-permeability oil and gas reservoirs. However, it is associated with low-pressure resistance and poor sealing performance. To enhance the performance of nylon cord rubber, a three-dimensional numerical model of the nylon cord rubber was established and its accuracy experimentally determined. The Plackett–Burman test, the Steepest climbing test and the Response surface method were used to acquire the polynomial response surface model connecting structural parameters with bearing and sealing pressure. Using genetic algorithms, optimal structural parameters of nylon cord rubber were determined depending on field operation. The reliability of the optimized results was verified by laboratory tests. It was shown that after optimization, the bearing capacity of the expandable packer increased by 25% while the sealing performance increased by 66%. In addition, the bearing pressure was 70 MPa while the sealing pressure was 50 MPa. These measurements effectively met the on-site requirements of high-pressure and fine fracturing in low-permeability oil and gas reservoirs.