A transient model for micro-elastohydrodynamic lubrication with three-dimensional asperities in line contacts is presented in this paper. To take into account the effect of non-Newtonian behavior of lubricant, the Ree-Eyring viscous constitutive equation is employed in deriving Reynolds equation. The numerical solution of this model is based on an implicit finite difference scheme with under relaxation. Numerical simulation results show that the pressure bump caused by an asperity or asperities depends not only on asperity height and orientation but also on asperity dimension. The increase in asperity dimension decreases the pressure bump. The decrease in load and increase in sliding speed increases pressure bump.