The current system associated with the boundary of plasma bubbles in the Earth's magnetotail has been studied by employing Cluster multi-point observations. We have investigated the currents in both the dipolarization front (DF, leading edge of the plasma bubble) and the trailing edge of the plasma bubble. The distribution of currents at the edge indicates that there is a current circuit in the boundary of a plasma bubble. The field-aligned currents (FACs) in the trailing edge of the plasma bubble are flowing toward the ionosphere (downward) on the dawnside and away from the ionosphere (upward) on the duskside, in the same sense as region-1 current. Together with previous studies of the current distributions in the DF and magnetic dip region, we have obtained a more complete picture of the current system surrounding the boundary of plasma bubble. This current system is very similar to the substorm current wedge predicted by MHD simulation models, but with much smaller scale.