Fiber Bragg gratings (FBGs) have been widely used in optical communication and optical sensing applications such that the chromatic dispersion measurement of FBGs is very important. In this thesis, we have proposed a simple measurement for characterization of FBGs using the common-path interferometric technique. We modified the un-balanced Michelson interferometer technique to develop the common-path interferometric technique by the similar Fourier-transform processing. In the common-path interferometer, the paths of the probe light and refer light are almost the same such that the environmental perturbation can be cancelled. We believe the repeatability and simplicity of this proposed technique is better than the un-balanced Michelson interferometer. We have repeatedly measured the group delay and reflection spectrum of a FBG filter. The experimental results excellently match the data measured by the optical network analyzer. Besides, the difference coming up with the result of the repeated measurement is very little which proves the repeatability is also great.