Results from a Ginga observation of the AM Her type object, H0538 + 608, carried out on 1988 February 7-10, are presented. During the first half fo the observation (pulsing state) the source showed periodic modulations caused by the white dwarf rotation, and the modulation profile was characterized by a flat top and flat bottom. During the second half, the source was in a remarkable flaring state and the periodic modulation disappeared. The dramatic change of the X-ray light curve is interpreted in terms of a change of accretion pattern between an eclipsing spot and a noneclipsing spot. The phase determined by the X-ray data coincides well with that expected from the optical polarimetry data by Mason et al., providing strong support for their tentative precise ephemeris. The spectrum is well described throughout by a thin thermal model including an iron K-line with equivalent width of some hundred eV, supporting the standard model for the hard X-ray emission region. The temperature in the pulsing state was found to change with the spin phase of the white dwarf. In the flaring state, the temperature showed a positive correlation with the source luminosity.