Electron states near the surface of small metal particle caused by an image charge (image-potential states) have been investigated. The wave functions were calculated and the energy spectrum of these states was found depending on particle size. To estimate the influence of static magnetic field on the image-potential states the model problem, in which electron is localized on a surface of a sphere in uniform magnetic field was solved. In this case the field dependence of the energy levels represents a complex level crossing structure.