This article describes the prediction of index of thrombus formation in shear blood flow by computational fluid dynamics with the Lattice Boltzmann Method (LBM), applying to backward-facing step flow, which is a simple model of shear flow in the rotary blood pumps and complicated geometry of medical fluid devices. Assuming that the blood flow is a multiphase flow composed of blood plasma and activated fibrinogen, the effects of surface tension and adhesion force to the wall were added to the LBM computational model. It was found that the thrombus formation in the backward-facing step flow occurred just after the reattachment point and behind the step. These results corresponded to our observation results of thrombus formation. For the thrombus formation in every case of blood flow to be predicted, effects of threshold level of physical parameters such as shear rate and adhesion force (effective distance from the wall) were estimated. Moreover, it was also found that the predicted adhesion point on the wall agrees with the visualization of thrombus formation by predicting proper thresholds.