We compile a sample of 38 galaxy clusters which have both X-ray and strong lensing observations, and study for each cluster the projected offset between the dominant component of baryonic matter center (measured by X-rays) and the gravitational center (measured by strong lensing). Among the total sample, 45% clusters have offsets >10". The >10" separations are significant, considering the arcsecond precision in the measurement of the lensing/X-ray centers. This suggests that it might be a common phenomenon in unrelaxed galaxy clusters that gravitational field is separated spatially from the dominant component of baryonic matter. It also has consequences for lensing models of unrelaxed clusters since the gas mass distribution may differ from the dark matter distribution and give perturbations to the modeling. Such offsets can be used as a statistical tool for comparison with the results of Lambda-CDM simulations and to test the modified dynamics.