Nowadays, many scientists work on the geometry change between source-to-detector arrangement to calibrate the 3”× 3” γ-ray NaI(Tl) detector based on the available sample shape in the laboratory. The calculated full-energy peak efficiency is more sensitive in radiation activity determination and can be estimated build on complex analytical and numerical techniques. In the present study, the full-energy peak and total efficiencies beside the peak-to-total ratio (P/T) for γ-ray NaI(Tl) detector concerning vertical hexagonal ^152Eu radioactive source is calculated for all γ-rays involved in the cascade and estimate the suitable correction for coincidence summing effects (COI) by mean of the numerical simulation method (NSM). The extra factors which cause the γ-ray attenuation taken into consideration as well, such as, source composition materials, “self-attenuation within the source itself”, the detector end cap with the other supporting materials around the detector crystal, the source container material, and the holder used during the measurement process. The theory of this methodology depends on the efficiency transfer technique; calculate the effective solid angle, that be positioned in between the source-to-detector system, besides estimating the path lengths of the γ-rays inside the hexagonal ^152Eu radioactive sources and the active medium inside the detector itself as well. The results gained in the present work gave an agreement between simulation and measured data. The results show that to improve the accuracy of the γ-rays detector efficiency, many technical and methodological aspects of the present method are fitting and possible for applications inside the radiation laboratory, industrial, and medical sectors.