A global computer simulation of the interaction of the solar wind with the earth's magnetosphere was executed by using a three-dimensional magnetohydrodynamic model. As a result, we were able to reproduce quasi-steady-state magnetospheric configurations and a Birkeland field-aligned current system which depend on the polarity of the z component of the interplanetary magnetic field (IMF). Twin convection cells and a dawn to dusk electric potential of 30--100 kV appeared at the equator in the magnetosphere. Four types of field-aligned currents were observed. Region 1 and 2 field-aligned currents generated for all IMF conditions were 0.6--1.0¿106 A and 0.15--0.61¿106 A, respectively, in the total current. Region 1 currents at high latitudes are generated from the field-aligned vorticity at the flanks through a viscous interaction and are strengthened by a twisting of open magnetic field lines in the tail region for southward IMF. On the other hand, the low-latitude region 2 currents probably are generated mainly from the inner pressure gradient of the plasma sheet. The region 1 current obtained from the simulation was in good agreement with an estimate from our theoretical analysis of the localized Alfv¿n mode. The other two types of field-aligned currents are the dayside magnetopause currents in the dayside cusp region, which increase for northward IMF, and the dayside cusp currents for southward IMF. The cusp currents are associated with a twisting of open magnetic field lines in the magnetopause region.