We have performed general relativistic hydrodynamics (GRHD) simulations of 2D discs orbiting around spinning black holes and prone to the Rossby Wave Instability (RWI). We show that the RWI can develop at any location in the disc and for any spin parameter. After recovering the overall patterns of the instability in this general relativistic context, we have analysed its development and identified some modifications induced by the combined effects of the relativistic rotational profile of the disc and local time dilatation that affects the propagation of waves in the disc. We have found in particular that the saturation level of the instability increases significantly when RWI occurs in the very close vicinity of fast-rotating black holes where general relativistic effects are strong. Such finding suggests that even more strongly than in the case of Schwarzschild black-hole, it is necessary to complement such GRHD simulations with a full GR ray-tracing processing in order to provide synthetic observations of the disc in the distant observer frame.