  In this paper, we validate the boundary layer theory for 2D steady viscous
incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0,
L]\times\mathbb{R}_+\}$ under the assumption of a moving boundary at $\{Y=0\}$.
The validity of the boundary layer expansion and the convergence rates are
established in Sobolev sense. We extend the results for the case with the shear
outer ideal MHD flows [3] to the case of the nonshear flows.
