We present the lunar wake current systems when the Moon is assumed to be a non-conductive body, absorbing the solar wind plasma. We show that in the transition regions between the plasma void, the expanding rarefaction region, and the interplanetary plasma, there are three main currents flowing around these regions in the lunar wake. The generated currents induce magnetic fields within these regions and perturb the field lines there. We use a three-dimensional, self-consistent hybrid model of plasma (particle ions and fluid electrons) to show the flow of these three currents. First, we identify the different plasma regions, separated by the currents, and then we show how the currents depend on the interplanetary magnetic field direction. Finally, we discuss the current closures in the lunar wake.