The semiconductor optical amplifier (SOA) is the key device for all optical signal processing, and the principle mechanism is its nonlinearity, which heavily depends on its group velocity dispersion (GVD). Based on the Kramers-Kronig relation, the relationship between GVD and the optical gain is obtained. A simple scheme to measure the GVD of the SOA is proposed with some computations from the measured gain spectra, and it is verified with the comparison between the analytical simulations and the measurements under the condition of small signal input. The dispersion is relatively flat in the range of 1530~1610 nm, and lightly depends on the input power and the injection current. The peak-gain wavelength and zero-dispersion wavelength red-shift with the input power increasing and blue-shift with the injection current increasing, and the zero-dispersion wavelength is greater than the peak-gain wavelength.