In this paper, we investigate the nonlinear stability threshold for the shear flows of the generalized magnetohydrodynamic (GMHD) equations on \({\mathbb {T}} \times {\mathbb {R}}\) . We prove the nonlinear stability of the shear flow \(\left( U_s, B_s\right) =\left( (e^{-t\nu \partial _{y}^4}U(y),0)^{\top },(\alpha ,0)^{\top }\right)\) with the initial data of the shear flow (U(y), 0) close to the Couette flow (y, 0). For sufficiently large \(|\alpha |\) , we prove that when the initial perturbations satisfy \(\Vert (u_{in},b_{in})\Vert _{H^{N+1}}=\epsilon \ll \nu ^{\frac{7}{10}+{\tilde{\delta }}}\) for any fixed \({\bar{\delta }}>0\) , here \(\nu\) is a positive real parameter, then for all \(t> 0\) , the global solution of the 2D GMHD equations remains \(\nu ^{-\frac{1}{5}-\frac{{\bar{\delta }}}{2}}\) \(\epsilon\) -close to \(U_s=(e^{-t\nu \partial _{y}^4}U(y),0)^{\top }.\)
