In cross-media color image reproduction, gamut mapping is needed due to gamut difference among different media. The first step of gamut mapping should be the determination of gamut boundaries of each medium involved, no matter what kind of mapping algorithm is to be used. It may be expected that an analytical expression for a boundary is preferable to a set of discrete data, since it would make the determination of the intersection point between a boundary and a "mapping line" easier and faster. This paper describes LCD display gamut boundary surfaces with a form of Zernike polynomial. In CIE1976L*a*b* color space, each color point on the boundary can be expressed as L*=L*(a*,b*) and every boundary can be expanded into a series of Zernike polynomials with appropriate coefficients. These coefficients can be obtained with sufficient experiment data of boundary points and existing algorithms. Experiments have been executed for a LCD display with(R,G,B) as its input. The 6 boundaries in RGB space would be formed respectively by (0,G,B),(R,0,B),(R,G,0),(255,G,B),(R,255,B) and (R,G,255) where each of R,G,B varies from 0 to 255. Then 6 corresponding sets of Zernike coefficients are calculated, based on about half of the measured L*a*b*'s for each boundary. A comparison between original measured data and the data predicted by Zernike polynomials shows that, not only for the data that have been used to calculate the coefficients, but also for those not used, the differences are acceptably small even negligible with only a few exceptions.