  We study the edge spin current and spin polarization in a two-dimensional
electron gas with spin-orbit coupling in the presence of a perpendicular
magnetic field. The edge effect removes the degeneracy of Landau levels due to
the competition between the Rashba coupling and the Zeeman splitting, which
exists in the bulk. Large spin edge current and non-linear response to an
electric field are found when the two levels are degenerated in the bulk. It is
found that he spin current is proportional to spin polarization along the
y-direction in an finite magnetic field, which provides a way to extract the
spin current in the system.
