Topological charge susceptibility w the MathML source">χt for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for w the MathML source">χt with values decreasing from w the MathML source">(188(1) MeV)4 to w the MathML source">(67(3) MeV)4 as the temperature increased from zero temperature to w the MathML source">1.9Tc which demonstrates the existence of topological excitations far above w the MathML source">Tc. The 4th order cumulant w the MathML source">c4 of topological charge, as well as the ratio w the MathML source">c4/χt is also investigated. Results of w the MathML source">c4 show step-like behavior near w the MathML source">Tc while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.