To assist with the color system design of a four-primary color display, it is necessary to build up a four-primary color simulation platform displayed on a wide color gamut red, green, blue (RGB) monitor. A new four-primary color conversion algorithm that is able to simulate four-primary color appearance built on a wide color gamut RGB monitor is proposed. The designed four-primary color system is composed of red, green, blue primary colors based on sRGB standard and the addition of the fourth primary color. The simulated fourth primary colors are selected from Kodak Wratten color filters, which CIE U'V' chromaticity coordinates are located in the range between the sRGB triangle gamut and the Adobe RGB (1998) triangle gamut. The four-primary color conversion algorithm is designed to be implemented on the Adobe RGB (1998) platform to simulate four-primary color appearance. The linear programming to formulate the convex optimization problem, which is named linear color convex combination, is introduced to establish a color conversion algorithm between the four-primary color signal and the corresponding color stimulus. The four-primary color conversion is also applied to build up four-color separation channels, which can simulate four-color channels shown on the Adobe RGB (1998) platform. It is demonstrated that the proposed color conversion algorithm can perform well on four-color channels displayed on the Adobe RGB (1998) platform. Meanwhile, the optimal four-color signals can be determined according to the tonal smoothness evaluation based on edge detection by Prewitt or Sobel operation.