The time evolution of beam properties in an electron bunch with the duration of a nanosecond was measured with a time resolution of several tens of picoseconds. A combination of horizontal and vertical slits cuts the beamlet from the original beam, with the current waveform of the beamlet measured using a fast wall-current monitor. The reconstruction of the waveform data obtained by scanning these two slits over the entire beam area provided the time evolution of the spatial profile. A similar measurement using two horizontal (vertical) slits separated by a certain distance also provides the time evolution of the phase-space profile. Using this method, the initial beam extracted from the CeB6 thermionic electron gun of the x-ray free-electron laser (XFEL) SACLA was evaluated. Although the slice emittance in the bunch was measured to be constant, the centroid of the spatial profile moved in the transverse direction by a few hundred micrometers in the 0.6ns flat-top region. This movement arises from the temporal variation in the rectangular high-voltage pulse of the beam chopper and can cause an increase in the projected emittance. These measurements are important for evaluating the conditions of the initial beam emitted from the cathode and processed downstream of the gun. Hence, the proposed diagnostic system will play an important role in developing an extremely low-emittance electron beam or an artificial electron beam with a multi-bunch or micro-bunch structure that enhances the brightness of the XFEL light.