The data of electron scattering factor for all neutral atoms, given in International Tables for X-Ray Crystallography in the range of sinθ/λ from 0.0 to 2.0 have been fitted by use of the damping least square method to an analytical formula with nine parameters as f(s)=sumfrom i=1to4 (aie-bis))+c. A relative deviation factor R=sumfrom k=1toN (|fok-fok|)/sumfrom k=1toN (fok) is served as the criterion of the relative deviation between the calculated and the observed values of the atomic scattering factor. The calculation shows that the relative deviation factors R for all atomic factors are approximately equal to 10-3. All parameters and corresponding relative deviation factors are tabulated. The maximun errors, the mean error, the mean square error and the summation square deviation are also given.