Numerical method is applied to the investigation of the GAM damping rate with the finite κ effects included. It is found that generally the damping rate given by the analytical method is smaller than that given by the numerical method, and the analytical damping rate has good approximation in the high q region (q > 4). The difference between the analytical and numerical damping rates increases with the increasing kρi. However, for the short-wavelength case (κρi= 0.2), the analytical methods are only good enough around q=4 because of the slow convergence of Bessel function with the large variable.