As an oceanic plate cools with time, the bottom part of the plate may undergo gravitational instabilities and lead to sub-lithospheric small-scale convection (SSC). While numerous previous studies have examined the dynamics of SSC below a fixed top boundary, in this study we investigate the effects of shearing due to plate motion on the onset and time evolution of SSC with 2-D and 3-D finite element models with a prescribed surface plate motion and a Newtonian rheology. Our 3-D models show that plate motion moderately enhances the SSC that displays plate-motion-parallel convective roll-structures. However, plate motion significantly hinders SSC in 2-D models with plate motion that produces plate-motion-perpendicular convective roll-structures. In spite of moderate influences of plate motion on the dynamics of SSC, our results suggest that for Newtonian rheology the onset time of SSC predicted from previous studies with a fixed top boundary is to the first order valid.