In order to measure jitter of gain-switched laser precisely, we analyze theoretically the math model and measurement principle of harmonic spectrum analysis used to measure laser pulse jitter. The error in pulse jitter measurement, which based on power spectrum measurement and was established by David A. Leep etc., is corrected. The universal math formula for measuring pulse jitter was deduced and the power spectrum of pulse in different conditions was numerically simulated. The pulse jitter of gainswitched Fabry-Perot laser with external cw-light injection was experimentally investigated by using harmonic spectrum analysis. The time jitter is 0.905 ps and amplitude noise is 2.83%. Compared with the outcome of sample oscilloscope measurement, it indicates that the harmonic spectrum analysis measurement is more precise and the accuracy is up to the magnitude of fs in the case of small jitter high repeat frequency.