Chirped fiber grating (CFG) is an important device that can be used to realize dispersion compensation of a fiber communication system and filter signals at the same time. Besides the ordinary way used to measure the spectrum properties of FBGs, an accurate method of measuring dispersion is crucial to specifying CFGs. This paper presents a simple system to suit the needs. The simple system is mainly composed of two facilities: a tunable laser and a lightwave component analyzer. In the system, a wavelength resolution of 1 pm and a phase resolution of 0.010, i.e. about 0.1 ps for time delay are obtained. The system can also be used in the measurement of the optical spectrum of the fiber grating.