A new method for measuring the birefringence dispersion in polarization-maintaining fibers (PMFs) with high sensitivity and accuracy is presented. The method employs white-light interferences between two orthogonally polarized modes of PMFs. The group birefringence of the fiber is calibrated first. Then the birefringence dispersion and its variation along different fiber sections are acquired by analyzing the broadening of interferograms at different fiber lengths. The main sources of error are investigated. Birefringence dispersions of two PANDA fibers at their operation wavelength are measured to be 0.011\text{\hspace{0.17em} ps}/\left(\text{km \hspace{0.17em} nm}\right) and 0.018\text{\hspace{0.17em} ps}/\left(\text{km \hspace{0.17em} nm}\right) . A measurement repeatability of 0.001\text{\hspace{0.17em} ps}/\left(\text{km \hspace{0.17em} nm}\right) is achieved.