A time-dependent two-dimensional MHD model of the ionosphere of Venus has been developed in order to study the magnetized ionosphere of Venus. The time-dependent continuity, momentum, and magnetic induction equations are solved self-consistently. Using this model, two-dimensional profiles of magnetic fields, electron densities, and velocities are obtained. It is found that the calculated horizontal velocities in the magnetic barrier are of the order of 10 km/s, which is consistent with the Pioneer Venus Orbiter (PVO) observations. Horizontal and vertical variations of the electron density, and the magnetic field are reproduced reasonably well. It is shown that above 240 km, both vertical and horizontal flows play an important role in transporting magnetic flux as well as in determining electron density profiles. Below 240 km, on the other hand, the behavior of the magnetic field is controlled primarily by the vertical motion because the horizontal transport is inhibited by the ion-neutral drag in the lower region. The overall magnetic field profiles in the model are quite similar to those of one-dimensional MHD models. The calculated electron densities of the nightside ionosphere are smaller than those for unmagnetized conditions because of less plasma transport from the dayside. ¿ American Geophysical Union 1996