Under the mutual influence of characteristic X-rays of the light elements and the measured elements, the measured X-rays’ fluorescence spectra will be seriously overlapped due to the restricted energy resolution of the instrument. This paper proposes a new method for analyzing EDXRF spectra by taking the chromatographic resolution Rs as an index to calculate the degree of spectral peak overlap and the overlapping peaks with Rs below 0.3 as the research object. First, this thesis introduces the peak sharpening method based on the fourth derivative in detail, and proposes the error wavelet transform. In addition, the new method was verified on simulated X-ray fluorescence spectroscopy. The simulation results show that when Rs=0.27, neither of the two methods can realize the analysis and identification of the overlapping spectral peaks; however, the processing by the 4-order peak sharpening method not only retains the peak position characteristics of the original signal, but also leads to increased Rs. Therefore, the resolution of the simulated overlapping peaks can be realized by adjusting the weight of the 4-order peak sharpening method to complete the initial sharpening of the overlapping peaks with low resolution, and then performing the error wavelet transform on the sharpened signal. Moreover, the combined new method (sharpening error wavelet transform) was proved to have a strong resolution ability for overlapping spectral peaks with very low resolution. Then, the superimposed Gaussian function was used to simulate the two sets of overlapping spectral peaks, which are the overlapping spectrum of the Kβ energy peak of Mn and the Kα energy peak of Fe (Rs=0.19) and the overlapping spectrum of the Kα energy peak of Al and its Kβ energy peak (Rs=0.11). The overlapping peaks were resolved by processing the spectral lines with the new method, and the result proved that the method is feasible for overlapping spectral peaks with extremely low resolution. Finally, the measured EDXRF spectrum was analyzed by sharpening the error wavelet, and comparative experiments were carried out by resolving three specific low resolution overlapping peaks. The results show that the method successfully resolves and identifies low-resolution overlapping peaks. This thesis aims to propose a practical and innovative method, and experiments show that the sharpening error wavelet transform is the cure, which can effectively decompose the overlapping spectral peaks with very low resolution.