We present a three-dimensional (3-D) numerical ideal magnetohydrodynamics (MHD) model, describing the time-dependent expulsion of plasma and magnetic flux from the solar corona that resembles a coronal mass ejection (CME). We begin by developing a global steady-state model of the corona and solar wind that gives a reasonable description of the solar wind conditions near solar minimum. The model magnetic field possesses high-latitude coronal holes and closed field lines at low latitudes in the form of a helmet streamer belt with a current sheet at the solar equator. We further reproduce the fast and slow speed solar wind at high and low latitudes, respectively. Within this steady-state heliospheric model, conditions for a CME are created by superimposing the magnetic field and plasma density of the 3-D Gibson-Low flux rope inside the coronal streamer belt. The CME is launched by initial force imbalance within the flux rope resulting in its rapid acceleration to a speed of over 1000 km/s and then decelerates, asymptotically approaching a final speed near 600 km/s. The CME is characterized by the bulk expulsion of ~1016 g of plasma from the corona with a maximum of ~5 ¿ 1031 ergs of kinetic energy. This energy is derived from the free magnetic energy associated with the cross-field currents, which is released as the flux rope expands. The dynamics of the CME are followed as it interacts with the bimodal solar wind. We also present synthetic white-light coronagraph images of the model CME, which show a two-part structure that can be compared with coronagraph observations of CMEs.