The convection of plasma in the closed field region of the Earth's magnetosphere is an important consequence and a diagnostic of the coupling of solar wind momentum and energy into the magnetosphere. In the outer regions the nature of the flow can help to distinguish between different coupling processes; for example, between (1) a global reconnection process between closed geomagnetic field and the interplanetary magnetic field (IMF), or (2) a local diffusive-viscous interaction. In the inner magnetosphere, the convection is responsible for both energization and redistribution of energetic and thermal plasmas. This paper presents the first results for convection of plasma in the closed field magnetosphere derived from a self-consistent, three-dimensional, magnetohydrodynamic simulation model of the Earth's magnetosphere. The results are shown as electric potential patterns in the equatorial plane. The equipotential contours, which are interpreted as plasma streamlines, demonstrate that line reconnection between closed geomagnetic field and the IMF is the dominant coupling process for southward IMF in the parameter range studied. Results are presented from three simulations, that is, southward, northward, and duskward IMF. For the southward IMF case, the quasi-steady cross polar cap electric potential is essentially equal to the bow reconnection voltage. The results show that reconnection on the open/closed magnetic field boundary is important for northward IMF also. In this case, the reconnection process takes place at the two polar cusps, and is an inherently unsteady process even though it leads to a quasi-steady convection potential in the ionosphere. The implications of these results, for the nature of the solar wind magnetosphere coupling, are discussed. Moreover, the convection results are closely related to the polar Birkeland current systems, which are the self-consistent consequences of the coupling process and in turn create the ionospheric convection flow. ¿ American Geophysical Union 1996