To predict the luminescence spectrum of phosphor-coated white LEDs more conveniently and efficiently, GaN Blue LED chip and YH-S525M green phosphor and YH-C640E red phosphor from Hangzhou Yinghe Optoelectronic Materials Co., Ltd. were selected for preparing experimental samples. The monochromatic fluorescence spectra were measured respectively. The emission peak wavelength of the blue-chip is 453 nm, the emission peak wavelength of red and green phosphor is 631 and 526 nm respectively. The red and green phosphors were mixed with AB glue and coated on the blue-chip. The mass ratio of red and green phosphors was set as 1:3, 1.2:3, 1.4:3, 1.6:3, 1.8:3 and 2:3. The concentration of red phosphors was set as 7%, 9%, 11%, 13%, 15% and 17%. 3~5 samples were prepared under each proportion and concentration, and the luminescence spectrum of each sample was measured by HAAS-2000 high-precision fast spectral radiometer of Hangzhou Yuanyuan chromatography Co., Ltd. A total of 36 groups of SPD (spectral power distribution) data were obtained by normalizing the relevant data. The white light spectrum was regarded as the linear superposition of blue, green and red monochromatic fluorescence spectra. The corresponding emission spectrum was directly selected for blue and red peak terms, while two Gauss linear equations were used for fitting the green peak term, and the intensity determined the coefficient. Therefore, a prediction model of the white light spectrum was established. The circular search algorithm calculated the optimal values of the model parameters under 36 groups of experimental conditions, and the model’s goodness of fit was tested. R² ranged from 99.33% to 99.88%. Then, the partial least squares regression method was used to establish the regression equation between the mass ratio, concentration of phosphors and the model parameters. Finally, a new method that can accurately predict white LEDs’ emission spectrum coated with red and green phosphors was obtained. The SPD of a group of newly prepared samples was used to test the prediction effect. The goodness of fit of the predicted spectrum is 99.62%, which proves that the prediction effect of this method is good. Based on the physical mechanism of phosphor-coated LEDs, the mathematical relationship between the mass ratio, concentration of phosphors and the white light spectrum is established more simply and effectively. Meanwhile, the interaction between the two phosphors was analyzed, and the broadening effect of the green phosphor spectrum was introduced to the prediction model. There is good universality, and this method provides a new idea for optimising the light source parameters of the phosphor-coated LEDs.