We present linear stability analysis of a pressure-driven flow in a fluid-layer overlaying porous media in the presence of a Couette component introduced by an upper impermeable wall. We model the flow dynamics in the porous media by the Brinkman equation and couple it with the Navier–Stokes equation for flows in the fluid-layer. The effect of the Couette flow component on flow stability is discussed in detail with varying the permeability and the relative thickness of the fluid to porous layers. The results show that the effect changes from destabilizing to stabilizing at a certain velocity of the upper wall. This velocity, called the cutoff velocity, is highly dependent on the porous medium characteristics. The cutoff velocity drops as the permeability of the porous surface decreases or the fluid layer thickness increases. Imposing a Couette flow shifts the instability mode from fluid mode to porous mode due to generation of vortices at the interface when the porous layer approaches an impermeable wall. We also performed energy budget analysis to provide a physical interpretation for the behavior of the flow. We found that the energy production due to the Reynolds stress causes the disturbances to grow which consequently triggers the instability.