To search for giant X-ray pulses correlated with the giant radio pulses (GRPs) from the Crab pulsar, we performed a simultaneous observation of the Crab pulsar with the X-ray satellite Hitomi in the 2-300 keV band and the Kashima NICT radio telescope in the 1.4-1.7 GHz band with a net exposure of about 2 ks on 2016 March 25, just before the loss of the Hitomi mission. The timing performance of the Hitomi instruments was confirmed to meet the timing requirement and about 1000 and 100 GRPs were simultaneously observed at the main pulse and inter-pulse phases, respectively, and we found no apparent correlation between the giant radio pulses and the X-ray emission in either the main pulse or inter-pulse phase. All variations are within the 2 σ fluctuations of the X-ray fluxes at the pulse peaks, and the 3 σ upper limits of variations of main pulse or inter-pulse GRPs are 22% or 80% of the peak flux in a 0.20 phase width, respectively, in the 2-300 keV band. The values for main pulse or inter-pulse GRPs become 25% or 110%, respectively, when the phase width is restricted to the 0.03 phase. Among the upper limits from the Hitomi satellite, those in the 4.5-10 keV and 70-300 keV bands are obtained for the first time, and those in other bands are consistent with previous reports. Numerically, the upper limits of the main pulse and inter-pulse GRPs in the 0.20 phase width are about (2.4 and 9.3) × 10-11 erg cm-2, respectively. No significant variability in pulse profiles implies that the GRPs originated from a local place within the magnetosphere. Although the number of photon-emitting particles should temporarily increase to account for the brightening of the radio emission, the results do not statistically rule out variations correlated with the GRPs, because the possible X-ray enhancement may appear due to a >0.02% brightening of the pulse-peak flux under such conditions.
