The ability to resolve overlapping and weak peaks is the key index to measure the peak-finding ability of X-ray fluorescence spectroscopy. It is difficult for common peak-finding methods to simultaneously satisfy higher peak resolution ability and weak peak recognition ability. It is difficult to identify all characteristic peaks in X-ray fluorescence spectra of complex geological samples by a single common peak-finding method. Through the analysis of the derivative method, wavelet transform method and other classical peak-finding methods, we can see that derivative method has a strong ability to identify weak peaks, but the smoothness of the spectrum affects the results of peak-finding; wavelet transform method has a strong ability to distinguish overlapping peaks, but the choice of wavelet decomposition scale affects the results of peak-finding. In this paper, an adaptive peak-finding algorithm of X-ray fluorescence spectrum based on the derivative method and wavelet transform method is proposed. In the algorithm, continuous wavelet transform is applied to the original spectrum to obtain the wavelet transform coefficient spectra of different decomposition scales; then the first derivative peak-finding is performed on the wavelet transform coefficient spectra, and the results are combined; finally, the elements in the original spectrum are determined according to the energy scale of the X-ray fluorescence analyzer and the X-ray parameter table of element characteristics. In the process of peak finding, the algorithm does not need to smooth the original spectrum, nor does it need to determine the wavelet transform decomposition scale of the spectrum. The first derivative method, continuous wavelet transforms method, and the adaptive peak-finding algorithm was used to find peaks of the X-ray fluorescence spectrum of a standard sample. The experimental results show that the adaptive peak-finding algorithm has a high resolution of overlapping peaks and high recognition of weak peaks, which is better than the derivative method and the wavelet transform method in peak finding. The algorithm performs well in practical application.