Abstract: Gamma-ray spectrometry uses the X-ray and characteristic gamma-rays associated with 235U, 238U and their decay daughters in uranium samples for analytical calculations to achieve rapid and timely nondestructive detection of sample enrichment. As one of the methods for determining uranium enrichment by gamma-ray spectrometry, the relative detection efficiency calibration method has been commonly used in nuclear safeguards on-site inspections to measure the enrichment of samples. Its core is the relative efficiency self-calibration using multiple characteristic gamma-rays of ²³⁵U in the low energy region of 120-186 keV and the characteristic gamma-rays of ²³⁸U decay daughter ²³⁴Pam in the high energy region of 258-1 001 keV. In this paper, the relative detection efficiency of the detector was obtained using the Monte Carlo method based on the actual characterization results of a coaxial-type high-purity germanium detector, the fitting results and errors of three different types of fitting formulas in different energy region ranges were investigated. A comprehensive analysis of the effect of the fitting formulas from the low-energy region to the medium-high energy region on the relative efficiency of the characteristic peaks shows the logarithmic transfer series function performs better results among the three fitting formulas. During the on-site inspection, the aluminum and stainless steel shieldings of the sample and the self-absorption of the uranium dioxide and uranium hexafluoride body source have a certain impact on the relative detection efficiency curve. The specific influence and changing trend of these factors on the curve were studied, and the fitted curves for thicker shields and strong self-absorption were then corrected by adding correction factors. The results show that after adding the correction factor, the fitting error of the relative detection efficiency curve for different shielding and self-absorption cases is reduced from 2%-4% to 1%-2% at the characteristic peaks used for enrichment calculation. The results of this paper have reference value for the nondestructive assay of uranium enrichment in the on-site inspection of nuclear safeguards.