We numerically investigate a potential fault activation in Tarim Basin, west China, during hydraulic fracturing operations, by considering rigorous coupled flow and geomechanics. In this study, we find that the fault can be activated by water injection, when it is nearly critically stressed, being sensitive to small changes in stress. Lower cohesion, lower frictional angle, and higher injection rate can activate the fault more easily. Interestingly, the fault becomes activated away from the hydraulic fracture, before the injected water reaches the fault plane. Then, when the hydraulic fracture meets the fault plane, the injected water changes the effective stress of the fault significantly, causing large shear failure. We also calculate the magnitudes of the seismic moment, which are low, because only limited areas of the fault plane are failed. Thus, from this preliminary numerical study of Tarim Basin, we can possibly consider the fault activation as a reservoir stimulation technique for the Tarim Basin field.