Displays with a larger color gamut to represent the images of the small color gamut are emphasized in the display development trend recently. Resulting from the vigorous development of Light Emitting Diodes (LEDs), the solutions to enlarge the color gamut which is formed a polygon area by adding multiple primary colors are possible, easier and inexpensive considerably. Therefore, how to determine the Gamut Boundary Description (GBD) plays a significant role for the applications of the multiple primary color displays, where the primaries form a convex polygon in CIE xy space. The paper proposed a method to construct the three-dimension color volume of GBD from the two-dimension polygon gamut area precisely regardless of that how many multiple primary colors the displays have. The method is examined in detail by the simulations and experiments, and proved it to fulfill from tri-primary color device to N-primary color device.