The authors have investigated quasi-linear ion Landau damping of lower hybrid waves in an inhomogeneous plasma. To this end, they have simultaneously solved Maxwell equations and the ion kinetic equation, starting from the antenna and proceeding towards the centre of a plane-layered plasma. As a consequence of the development of a suprathermal tail in the ion distribution function, the efficiency of the absorption increases and the absorption region is found to shift to lower densities as the launched power increases. Absorption is always complete at the layer where the wave phase velocity equals about three times the local ion thermal velocity, usually somewhat before the linear turning point is reached.