Recent studies of lensing clusters reveal that it might be fairly common for a galaxy cluster that the X-ray center has an obvious offset from its gravitational center which is measured by strong lensing. We argue that if these offsets exist, then X-rays and lensing are indeed measuring different regions of a cluster, and may thus naturally result in a discrepancy in the measured gravitational masses by the two different methods. Here we investigate theoretically the dynamical effects of such lensing-X-ray offsets, and compare with observational data. We find that for typical values, the offset alone can give rise to a factor of two difference between the lensing and X-ray determined masses for the core regions of a cluster, suggesting that such "offset effect" may play an important role and should not be ignored in our dynamical measurements of clusters. ; Comment: 6 pages, 4 figures, 1 table, accepted for publication in MNRAS