A high-accuracy test system for the dispersion measurement of chirped fiber gratings has been developed. The principle is based on converting the difficult measurement of the phase delay of light into the simple measurement of microwave. In our novel configuration, a lightwave component analyzer is used for the measurement of the phase delay with high resolution and as frequency-tunable RF source. The test system has a wavelength resolution of 1 pm and a time-delay resolution of <1 ps. A linearly chirped fiber reflection grating and a Gaussian-apodized Bragg transmission grating have been tested with high resolution. Influences of noise in the measurements are also discussed and some new ideas are presented.