In this paper, we consider the initial boundary value problem of a class of one-dimensional magnetohydrodynamics (MHD) with viscous, compressible, and non-Newtonian flow. We prove the existence of the solution in the presence of the resistivity coefficient, obtain the convergence rate in L2-norm, and establish the blow-up criterion of the local strong solution in the presence of the resistivity coefficient. Moreover, the initial vacuum is allowed.