This study conducts a multi-scale analysis on the drag reduction (DR) in the fluid flow diluted with the polymers. A mesoscopic description of ensemble of elastic dumbbells using Brownian dynamics (BDS) is connected to the macroscopic description for the solvent Newtonian fluid using DNS [1]. In Horiuti \etal [2], non-affinity in which the motion of dumbbells does not precisely correspond to macroscopically-imposed deformation was introduced and its effect on DR was elucidated in homogeneous isotropic turbulence (HIT). This work aims to carry out assessment on the influence of shear on DR in non-affine viscoelastic turbulence placed under constant mean shear. It is shown that the occurrence of DR and its mechanism are in agreement with those in HIT. More drastic DR is achieved when non-affinity is maximum than in the complete affine case. This difference is attributable to the convective motions of dumbbells. In the complete affine case, the connector vector of dumbbell is convected as a contravariant vector representing material line element, whereas, when non-affinity is the largest, it is convected as a covariant vector representing material surface element. In the latter case, the dumbbells directs outward perpendicularly on the planar structures and exert an extra tension on vortex sheet, which leads to attenuation of energy cascade, causing larger DR. The effect of presence of the streaks on the alignment of the dumbbells is discussed.