Abstract: A new stable algorithm is presented for AstroMesh antenna structure with large deformation based on the parametric variational principle (PVP) and nonlinear finite element method. Firstly, a parametric variable with its related complementary equation is introduced to model the bilinear constitutive relations of cable elements, and so a unified description of bilinear constitutive model is obtained, which avoids the prediction that the cable is tensioned or relaxed for traditional algorithms. Then, the Lagrangian strain is applied to tackle the large deformation problem of the AstroMesh structure. The nonlinear equilibrium equations and complementary equations are established based on the nonlinear geometric finite element method and parametric variatianal principle. The Newton-Raphson scheme combined with Lemke algorithm is employed to solve the equations. Numerical examples are given to demonstrate the convergence and accuracy of the PVP method in this paper are better than those of the traditional method. The proposed method is particularly suitable for high-precision analysis and prediction for large deformation of AstroMesh antenna structure.