A measurement method for birefringence dispersion is proposed using geometric phase. The optical arrangement consists of a white light source, polarizer, sample, quarter-wave plate, rotating analyzer, such as in a Senarmont setup, and a spectrometer for the visible spectrum from 450 to 750 nm. The experimental setup achieves a phase shift via the geometric phase produced by a cyclic change of polarization state on a Poincaré sphere. We can select four points of geometric phase when the analyzer is set at –45, 0, 45, and 90 deg. It is mathematically demonstrated that these points of geometric phase are independent of wavelength from the calculation of spherical trigonometry drawn on the Poincaré sphere. The phase shifting technique using these four geometric phases is applied to measure birefringence dispersion. Polymer films and optical crystals as samples are experimentally demonstrated, and it is shown that the experimental results agree well with the known quantities of retardation in the visible spectrum.