In this paper, the effect of a magnetic field on non-Newtonian blood flow in a cavity driven by the motion of two facing lids has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). It was assumed that the viscosity of the blood flow is shear-dependent as the power-law model has been selected for the viscosity of the flow. This study has been performed for the certain pertinent parameters of Reynolds number (Re = 100, 400 and 1000), Stuart number (N = 0, 1,10 and 50) and power-law index (n = 0.6, 1 and 1.4) as the magnetic field is applied horizontally. Results show that the increment of Reynolds number augments the effect of the magnetic field on the non-Newtonian blood flow. Furthermore, the drop in the power-law index increases the influence of the magnetic field on the flow. (C) 2013 Elsevier B.V. All rights reserved.