  A Monte Carlo method based on the GEANT4 toolkit has been developed to
correct the full-energy peak (FEP) efficiencies of a high purity germanium
(HPGe) detector equipped with a low background shielding system, and moreover
evaluated using summing peaks in a numerical way. It is found that the FEP
efficiencies of $^{60}$Co, $^{133}$Ba and $^{152}$Eu can be improved up to 18\%
by taking the calculated true summing \mbox{coincidence} factors (TSCFs)
correction into account. Counts of summing coincidence $\gamma$ peaks in the
spectrum of $^{152}$Eu can be well reproduced using the corrected efficiency
curve within an accuracy of 3\%.
