To provide high-quality, intelligent, and healthy lighting sources, a linear dimming mixed lighting system is constructed using three-primary-color LED light sources. An optimization method for dimming and color mixing is proposed. The light chromaticity and light intensity of the mixed light source are set by color temperature and brightness level, which makes the mixed lighting effect more in line with the demand of "human-centric lighting". In the intelligent optimization of the system, the color temperature is converted into CIE $ {u}'{v}' $ chromaticity coordinates, and the brightness is converted into luminance to make the optimization calculations more accurate. The system adopts the linear dimming method, effectively avoiding the health and safety hazards caused by light source flicker, and effectively solves the problem of large linear dimming chromaticity drift with an optimization algorithm. Experiment results demonstate that the chromatic stability of the mixed light in the mixed lighting system is maintained within the first step of the CIE ${u}'{v}' $ chromaticity diagram in the color temperature range of 2000 K-8000 K. Moreover, the system exhibits imperceptible color deviation over the entire range of light intensity adjustments at the corresponding color temperature. This finding also indicates that linear dimming is better than the pulse-width dimming method in keeping the optical chromaticity stable. Theoretical exploration and experimental results demonstrate that the mixed lighting system is simple and feasible, with significant practical value.