In this paper, the optical conditins of a reflective multi-color STN-LCD based on electrical control of birefringence is designed on the poincare sphere. First of all, the angles of polarizer and analyzer for the best color purity are decided in the configuration without a retardation film. A retardation film is introduced for a bright white in the range of the applied voltage. The sretardation and the angle of the retardation film are also decided on the poincare shpere. The test cell is farbricated and its measured spectral transmittance and the CIE chromaticity diagram agree well with simulations.