A nonlinear quantum hydrodynamical model of simple metal surfaces is developed for predicting nonlinear corrections to the image potential acting on a highly charged ion moving near a planar surface. The classical image potential acting between a classical point charge, Z1e, and a metal surface may be derived, within a linear hydrodynamical model, as the virtual excitation of a surface plasmon due to the interaction with the external charge. On the other hand, a nonlinear quantum hydrodynamical model of the homogeneous electron gas has been recently developed to study second order corrections to the wake potential of fast charged particles passing through matter, and this model is now extended to study the bounded electron gas.