Multi-primary-color display technology has been an important technical route to achieve color gamut expansion, which improves display brightness and energy efficiency by adding white sub-pixels. To drive Red-Green-Blue-White (RGBW) displays, color gamut mapping is required. In order to make the color saturation theoretically consistent before and after color gamut mapping, the white sub-pixel grayscale value is usually deducted from values of chromatic sub-pixels in traditional algorithms, which greatly reduces the contribution of chromatic sub-pixels to brightness enhancement, resulting in a less overall brightness increase. In addition, there is currently few objective and intuitive evaluation index to evaluate the performance of algorithms.A mathematical model of color gamut mapping transformation was established by combining the general method of color gamut mapping in this paper. Two key parameters of the mapping rate-of-change function and the white sub-pixel driving function are proposed. According to the characteristics of RGBW color gamut mapping algorithm, a four-in-one evaluation index system was proposed, it includes the Average Brightness Magnification (ABM), the Average Chromatic Sub-Pixels Magnification (ACSM), the Average White Sub-pixel Ratio (AWSR), and the Average Saturation Ratio (ASR). Based on the evaluation index system, the Mapping Rate-of-Change Function and the White Sub-Pixel Driving Function were determined. A linear algorithm function was constructed based on evaluation index system, which was continuously adjusted to a quadratic function to reach the best effect, and a more efficient and simplified new color gamut mapping algorithm was realized. The proposed algorithm is designed to increase the contribution of chromatic sub-pixels to the brightness improvement of the image without deducting the white component and with maximizing the chromatic sub-pixels grayscale values, and it can also balance the AWSR and the ASR by adjusting the weight factor.Simulation images processed by the proposed algorithm is displayed on an RGB Flat Panel Display (FPD) to simulate algorithms effect. Furthermore, the physical verification is carried out on a projector that supports RGBW projection, and the imaging brightness under two platforms is measured respectively by using an image luminance colorimeter. The results show that the brightness of the proposed algorithm can be increased by 2.26 times and 2.59 times on flat panel display and projector platforms respectively. In terms of evaluation indices, the ABM of the proposed algorithm reached 2.304, the ACSM reached 1.677, the ABM reached 2.3 times that of traditional algorithms, and the contribution of the chromatic sub-pixels grayscale values to the brightness improvement reached 1.67 times that of traditional algorithms. The AWSR was 0.261, and the ASR was 0.733, which better balanced the overall brightness enhancement and saturation decrease of images. Simulation rendering pictures of each algorithm on an RGB flat panel display were also taken in the experiment, as well as actual pictures projected by an RGBW projector. Judging from these pictures, the proposed algorithm can significantly enhance the display brightness and have a good performance of color retention. The calculation results of evaluation indices, measurement results and simulation verification results are basically consistent, so the evaluation index system can better show the performance of the RGBW color gamut mapping algorithm. This study provides a reference for evaluation performance of RGBW algorithms and construction of new algorithms in the future, and providing new directions for color gamut mapping in multi-primary-color displays.