A new statistical fitting approach, named Statistical Distribution-Based Analytic (SDA) method, is proposed to fit single Gaussian-shaped K-alpha and K-beta X-ray peaks recorded by Si(PIN) and silicon drift detector (SDD). In this method, we use the discrete distribution theory to calculate standard deviation of energy resolution sigma. The calibration of sigma and energy (E) for two detectors between the energy ranges of 4.5-26 keV are also completed by measuring characteristic X-ray spectra of nineteen types of pure elements. With the spectrum fraction (SF) parameter proposed in this paper, the SDA method can be used to resolve overlapping peaks. In measured spectra, the Gaussian part of X-ray peaks can be fitted by a Gaussian function with two parameters, sigma and SF. This new fitting approach is simpler than traditional methods and it achieves relatively good results when fitting the complex X-ray spectra of national standard alloy samples detected by Si(PIN) and SDD detectors. The chi (r) (2) values are obtained for each spectrum to assess fitting results, and the SDA fitting method gives a preferable fit for the SDD detector.