A variational method is presented to calculate dynamic corrections to the image potential of a charged particle at a metal-vacuum interface and hence to calculate its binding energy. The response of the metal is treated within the plasmon approximation. As an application, a model for positron surface states on simple metals is studied. It predicts the existence of bound positron surface states in Al, Ga, Zn, Cd, and possibly other high-density simple metals. Further, the resulting localized positron state would have a lifetime 2 to 3 times longer than in the bulk.