The BL Lacertae object H0323+022 was observed in X-rays with Ginga on three occasions, in 1987 July, 1988 August, and 1991 August. In the 1987 observation, the source was relatively bright, and variable by a factor of 3 on time scales of several hours. The observed 2-20 keV energy flux ranged between 2.2 and 4.1 x 10(-11) ergs CM-2 s-1 during the variation. The X-ray spectra were well described by a power-law model without intrinsic photoelectric absorption, and the photon index varied between 1.3 and 1.9 as the intensity changed. The spectrum was much better correlated with the time derivative of the X-ray intensity than the intensity, itself, in such a way that the spectrum hardened when the intensity increased. A detailed analysis of this spectrum-intensity correlation indicates that variation in the higher-energy band (4.1-10.5 keV) precedes that in the lower-energy band (1.2-4.1 keV) by roughly 0.05 d. This supports the idea that X-ray emission from H0323+022 is of synchrotron origin. In the 1988 and 1991 observations, the source was rather faint and only marginally detected at a 2-20 keV flux level between 0.6 and 1.1 x 10(-11) ergs CM-2 S-1. On these two occasions no intensity variations were detected, and soft spectra with a photon index of more than 2.0 are indicated.