The least-squares variational method (LSVM) is used for determining trial wavefunctions representing low-energy positron-xenon elastic scattering, which are used to determine the positron lifetime. The trial function is taken to depend on several adjustable parameters, and is improved iteratively by increasing the number of terms. The bound state wavefunctions are obtained using Hartree-Fock-Slater method. The 2γ-rays annihilation rates of the positron in xenon atoms below Positronuim (Ps) formation threshold are calculated. Polarization potential Vpl (r) is applied to enhance annihilation rates and lifetime. The present results of annihilation parameters are consistent with semiempirical, theoretical and experimental results.