The deformation and breakup of a single liquid drop subjected to simple shear flow is studied numerically using a diffuse interface free energy lattice Boltzmann method. The effect of dispersed phase viscosity on the behavior of the drop at a drop Reynolds number Re= 10 is investigated over the range of viscosity ratios lambda = 0.1-2 (dispersed phase viscosity over continuous phase viscosity) with a focus on lambda < 1. For every lambda. the critical capillary number Ca-c for breakup is determined. For the range of lambda. considered, Ca-c decreases as lambda increases. Both the extent of deformation and the breakup mechanism depend on the viscosity ratio and the capillary number. At the highest subcritical capillary number, the drop becomes less elongated and more inclined towards the vertical axis as the viscosity ratio increases. The changes in the drop breakup process are examined as the capillary number increases from the lowest supercritical Ca similar to Ca-c, to 12, 1.5 and 2Ca(c). Drops break by the end-pinching mechanism, except for lambda=2 at Ca = 2Ca(c) where the drop undergoes capillary wave breakup. (C) 2014 Elsevier Ltd. All rights reserved.