It is always difficult to extract the single pure spectral data from the mixed gas spectrum with severe overlap. In order to obtain the ideal unmixing precision, an improved non-negative matrix factorization algorithm is proposed, in which the correlation constraint and smoothness constraint of the spectrum is introduced, and the iterative step size of the optimized gradient descent method is given to avoid the effects of algorithm convergence to local instability. The improved algorithm combines the decomposition error of the matrix and influence of the mixed spectral characteristics. The experimental data show that the demixing results obtained by the improved non-negative matrix factor can accurately resolve the characteristic peak shape of each source spectrum, and there is almost no mixed superimposed influence between the demixing results, which can satisfy the subsequent spectral recognition work.