A plethora of studies have investigated the motion of a liquid droplet in the vicinity of a smooth surface, incurred by shear flow, parabolic flow or gravity. However, there are few studies that consider the roughness of the surface that could affect the droplet motion. In this study, we employ a 3D spectral boundary element method for interfacial dynamics to examine the droplet translation, migration, and deformation in the vicinity of a rough surface due to shear flow. The roughness feature of the surface is comparable to the size of the droplet and is simulated with sinusoidal functions. Topologies of epoxy coating surfaces are also considered in the computations. The roughness and profile of the coating surface is obtained by atomic force microscopy. The computational results show that the surface roughness affects significantly the behavior of a deformable droplet near the surface, including its deformation and migration speed. In return, the dynamics of the droplet also influences the stress distribution on the rough surface. The results of this study could provide theoretical foundation in the prediction of particle induced erosion corrosion of organic coatings.