We have performed a stroboscopic measurement on the timing jitter of 2-MeV electron beams accelerated in a high-power free-electron laser injector. In order to measure the timing jitter, which is separated from the current fluctuation of the electron bunches, we devised and formulated a stroboscopic method. The derived formula relates the relative phase variations of electron bunches due to the jitters to the current variations, which form a voltage distribution as a result of their accumulation. After using an image dissector to measure both the voltage distribution and the bunch length, we could determine the timing jitter with the help of the formula. Finally, we discuss the results in detail and compare the jitter with that measured by using a wall current monitor.