We present a versatile and accurate chromatic dispersion measurement method for single mode optical fibers over a wide spectral range (200 nm) using a spectral domain white light interferometer. This technique is based on spectral interferometry with a Mach-Zehnder interferometer setup and a broad band light source. It takes less than a second to obtain a spectral interferogram for a few tens of centimeter length fiber sample. We have demonstrated that the relative group velocity, the chromatic dispersion and the dispersion slope of a sample fiber can be obtained very accurately regardless of the zero-dispersion wavelength (ZDW) of a sample after frequency dependent optical phase was directly retrieved from a spectral interferogram. The measured results with our proposed method were compared with those obtained with a conventional time-domain dispersion measurement method. A good agreement between those results indicates that our proposed method can measure the chromatic dispersion of a short length optical fiber with very high accuracy.