Abstract: In order to advance the convergence effect,a set of asymptotic equations of the atmospheric gravitational load Love Numbers are presented.Green's functions of atmospheric gravitation loading,describing the Earth deformation which includes horizontal and vertical displacements,horizontal and vertical accelerations and strain tensor,are derived out by evaluating the properly weighted sums of the load Love numbers.By taking into account of asymptotic expressions of the gravitation load Love numbers,the Green's functions are reformulated to make them converge faster.This may improve the accuracy of the Green's functions in piratical computation.The numerical results of Green's functions for the unit point mass at the heights of 0km,1km,20km,6km above the Earth's surface are listed in Table 3.