We propose the measurement techniques for the chromatic dispersion and the polarization-mode dispersion of the fiber grating devices in this project. Applying a Michelson interferometer, the time delay difference between the lights reflected by the fiber grating and the mirror can be measured. We use a broadband source and an optical spectrum analyzer, which are the popular instruments in the fiber-optic passive device companies, to measure the optical signal spectra in the measurement setups. Applying some signal processing skills, the dispersion curves of a fiber grating can be determined. We hope using the development of the low-cost and high-accuracy measurement techniques, the cost of the fiber gratings can be reduced, and the competition of the fiber grating products can be increased. Furthermore, the associated measurement techniques may be the easy-setting and low-cost measurement systems in the production line of the fiber-optic passive device companies.