Excitation of energetic-particle (EP)-induced geodesic acoustic modes (EGAMs) by velocity space anisotropy is investigated taking into account the coupling to the GAM continuous spectrum. The response of EPs is studied nonperturbatively and both local and nonlocal dispersion relations of EGAM are derived assuming a single pitch angle slowing-down energetic ion equilibrium distribution function. For a sharply localized EP source, it is shown that the mode is self-trapped where the EP drive is strongest, with an exponentially small damping due to the tunneling coupling to the GAM continuous spectrum.