Consider the Sobolev stability of shear flow in the 2D incompressible magnetohydrodynamics (MHD) equations with background magnetic field on . We first consider the case where the shear flow is Couette flow, and on this basis, extend the analysis to shear flow near Couette. More precisely, we show that when the initial datum of shear flow satisfies , and the initial perturbation satisfy for any fixed , then the solution of the 2D MHD equations remains -close in to for all .