According to the LED spectra measured in the rated current, Gauss distribution function and asymmetric Gaussian distribution function methods are used to simulate the individual LED spectrum. Based on this mathematical model, 32 LEDs are used to synthesize arbitrary spectral distribution of the light source. Processing the spectral data with multiple linear regressions, CIE illuminant A and CIE illuminant D65 are simulated. The results show that for each LED, different Gauss models should be used. The simulation results are quite satisfying. However, there is a difference between the simulation results and the experimental results. The spectral evaluation indices of fitted both CIE illuminant A and CIE illuminant D65 do not exceed 2.5%. But in experiment, because of the changes of the peak wavelength and the FWHM caused by the current, the spectral evaluation indices of fitted CIE illuminant A and CIE illuminant D65 are around 5%.