Traditional Chinese paintings (TCPs), which are characterized by enormous storage and high value, are prone to suffering from radiation damage from museum illumination, such as color fading, discoloration, and color vanishing, especially for the most light-sensitive traditional Chinese paintings that are painted with organic pigments (op-TCPs). Thus, the development of light sources that minimize the damage to TCPs is essential. Meanwhile, the color quality of light sources is also of great importance, and there is a lack of methodology for obtaining light sources with optimized spectra to simultaneously achieve the protective effect and ensure the color quality. Here, changing curves of the CIE DE2000 color differences of pigments were shown as a function of the exposure duration by calculating the periodically measured color parameters in a long-term illumination experiment under four monochromatic lights. Relative spectral responsivity functions of the op-TCPs were deduced by fitting the experimental data and obtained the corresponding equal-illuminance relative damage formulas. Then, damage laws to the op-TCPs and the lowest color damage spectral power distributions that satisfy the color quality requirements of a four-primary white LED model were obtained. Our results can provide the theory and application basis to manufacture white LEDs that are suitable for illuminating op-TCPs; the method can be further used in preparing white LEDs for other cultural relics.