The MCNP code was utilized to assess the operational status of an N-type high-purity germanium (HPGe) detector and to evaluate its potential for a collimated and focused Prompt Gamma Neutron Activation Analysis (PGNAA) detection system. In order to calibrate the detector, a narrow beam γ collimator was designed to scan the detector in both axial and radial directions. The curvature of the crystal front edge and the non-uniform description of the detector dead layer (DL) were taken into account when adjusting the effective crystal size. A collimated 137Cs γ source was used to assess the detection efficiency in the scanning experiments. Monte Carlo studies were performed using 0.662 MeV γ rays, and separately, a uniform γ-ray energy distribution from 0 to 1.6 MeV. Lastly, the effects of a collimation aperture with different sizes and different incident directions were considered to discuss the relationship between the spatial resolution and suitable measurement scenarios. Therefore, a detailed calibration method for non-uniform dead layers was introduced through a comparison between experiments and Monte Carlo simulations. This work reevaluates the performance of HPGe detectors and provides valuable data support for a detailed system design and γ spectroscopy analysis in future.