Recent observations have shown that coronal magnetic fields in the northern (southern) hemisphere tend to have negative (positive) magnetic helicity. There has been controversy as to whether this hemispheric pattern is of surface or sub-surface origin. A number of studies have focused on clarifying the effect of the surface differential rotation on the change of magnetic helicity in the corona. Meanwhile, recent observational studies reported the existence of transient shear flows in active regions that can feed magnetic helicity to the corona at a much higher rate than the differential rotation does. Here we propose that such transient shear flows may be driven by the torque produced by either the axial or radial expansion of the coronal segment of a twisted flux tube that is rooted deeply below the surface. We have derived a simple relation between the coronal expansion parameter and the amount of helicity transferred via shear flows. To demonstrate our proposition, we have inspected Yohkoh soft X-ray images of NOAA 8668 in which strong shear flows were observed. As a result, we found that the expansion of magnetic fields really took place in the corona while transient shear flows were observed in the photosphere, and the amount of magnetic helicity change due to the transient shear flows is quantitatively consistent with the observed expansion of coronal magnetic fields. The transient shear flows hence may be understood as an observable manifestation of the pumping of magnetic helicity out of the interior portions of the field lines driven by the expansion of coronal parts as was originally proposed by Parker (1974).