In order to analyze and measure the radioactive content of samples more accurately and conveniently, a Monte Carlo application software tool (Geant4) is used to obtain the full energy peak efficiency curve of high-purity germanium (HPGe) detectors and thus to simulate and correct it in the measurement of radioactive samples. In particular, the different characteristic energies of a detector are measured in response to a point source 25 cm away from the HPGe probe. The experimental detection efficiency of γ-rays is compared with the simulation detection efficiency, and the influence of the dead layer on the detector efficiency of the HPGe crystal surface is studied by means of Geant4 simulations. The detection efficiency of the model is corrected by modifying the thickness of the upper and lower dead layers in turn, and the parameters of the Monte Carlo geometric model of the detector are optimized. Thereafter, the simulated efficiency of the optimized model is again compared with the measured efficiency of the point source, and the full energy peak efficiency curve of the HPGe detector in the range of 59.54‒1406 keV is obtained. The experimental measurement results show good agreement with the Monte Carlo simulations, exhibiting a relative error within 5%. The experimental results also demonstrate that the thickness of the dead layer on the surface of the HPGe crystal changes with the aging of the detector. After 7 years, the thickness of the dead layer increases from 0.5 mm to approximately 140 mm±0.05 mm.