Abstract: In this paper, a method for calculating elastic scattering cross section of low energy electron based on solving relativistic Dirac equation is given, the cross sections calculated by applying Thomas-Fermi-Dirac (TFD) potential and Hartree-Fock (HF)potential respectively are compared, the cross sections of elements C, Al, Cu, Ag, Au are calculated, the differences between Mott model. Pendry model and Rutherford formula are also compared and analysed.