We used the Monte Carlo simulation method to establish a detector response matrix and the non-negative least-squares method to deconvolute x-ray spectra. The simulation and experimental data verified the effectiveness of this method, and the influence of full-width at the half of the maximum calibration accuracy on the deconvolution results was investigated. The non-negative least-squares method had high accuracy and efficiency compared with others. The results showed that, except for Zn, the relative errors between the inversion and the standard values were less than 0.1% for the simulated spectra. For the experimental data, the relative errors were within 0.2%. The peaks with similar characteristic energies can be better distinguished in the deconvolution spectra, reducing the errors caused by overlapping peaks in subsequent analysis.