The spectrum analysis can be carried out via establishing the detector response function(DRF), to improve the automation level and the computation accuracy of the spectrum data processing. A general DRF model is established for Si-PIN detectors via the analysis of the X-ray physical detect procedure. The model contains four parts: a flat continuum shift from zero to full energy; a Gaussian shaped principal component of full energy peak; a Gaussian shaped Si escape peak; and an exponential tail on the low energy side of the full energy peak. Each part of the model, with a simple format, has a clear and definite physical meaning. Parameters are obtained by using the program, based on the Weighted Least-Squares(WLS) method. Nineteen elements' X-ray spectra in total are fitted in the study, and the fitting reduced chi-squares are also obtained simultaneously, which is in the range of 1.05-2.71. It is shown that this DRF model can represent the characteristic X-ray spectrum peak shape very well.