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A Monte Carlo method based on the GEANT4 toolkit has been developed tocorrect the full-energy peak (FEP) efficiencies of a high purity germanium(HPGe) detector equipped with a low background shielding system, and moreoverevaluated using summing peaks in a numerical way. It is found that the FEPefficiencies 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 thespectrum of $^{152}$Eu can be well reproduced using the corrected efficiencycurve within an accuracy of 3\%.

Summing coincidence in rare event gamma-ray measurements under an ultra-low background environment