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The modified sum-peak method estimates radioactivity by using only the peak and the sum-peak count rates. To verify the modified sum-peak method, the dependence of the full energy peak efficiency on the source-to-detector distance in a high-purity germanium detector system was studied using a Geant4 Monte Carlo simulation. The effect of the dead-layer in the germanium crystal was estimated by reference to experiments on 241Am and the relative efficiency of the detector. The peak efficiency dependence on the source-to-detector distance was compared between the simulation and measurements. The modified sum-peak method is discussed with respect to these peak efficiencies.