With the introduction of an automatically scanning grating monochromator, the rapid measurement of dispersion is realized, which greatly reduces the influence of the slow drift of carrier envelope offset frequency on the measurement accuracy, reduces the experimental complexity, and improves the dispersion measurement accuracy. In the experiment, the 815 nm Ti∶sapphire mode-locked laser is used as the light source and a home-made eight-mirror ring cavity is taken as a reference, the group delay dispersion (GDD) of a piece of 6.35 mm-thick fused silica plate is measured and the difference between the results and that from the theoretical value derived from the equation of Sellmeier is 1.2 fs2 with an only uncertainty of 0.5%. The GDD of the eight-mirror ring cavity under normal temperature and pressure condition is 28.8 fs2, smaller by 12 fs2 than the theoretical value, which is attributed to the coating inhomogeneity of the eight cavity mirrors.