Abstract: Based on the Skyrme energy density functional and the Thomas-Fermi expressions of the kinetic energy density, we use the restricted density variational method to calculate the neutron skin thickness for 208Pb, 112~124Sn, 48Ca, 96Zr, 18O with 47 Skyrme interactions available up to now. Comparing our calculated results with the experiment data, we explore the relations between the neutron skin thickness and the symmetry energy term of the equation of state(EOS) of nuclear matter. We find that the neutron skin thickness is sensitive to the nucleon-nucleon interaction and increases with the stiffness of the symmetry energy. Our study indicates that the model independent neutron skin thickness data are especially important for providing accurate information of the density dependence of the symmetry energy of nuclear matter. By calculating the neutron skin thickness of nuclei in the range of Z = 8 ~ 120, A = 5Z/3 ~ 3Z ,we find a linear relation between the neutron skin thickness and the isospin asymmetry degree δ: , which is in agreement with the result extracted from the measurements by antiproton annihilation method i.e.: . Using the data from antiproton annihilation method, we get the ranges of the slope , curvature of the symmetry energy near the saturated density (L, Ksym )and the symmetry energy coefficient as : L = 20 ~ 100MeV，Ksym =-256 ~ 70MeV, as = 30 ~ 35MeV. The Skyrme parameters SLy0-SLy10，SkM*，SkP，SLy230a，SkMP，SKT1-3，SkI3，MSk1-2，SII are in the above ranges.

Key words: Equation of State, Asymmetry Energy, Neutron Skin Thickness