Plasmons, the collective excitations of electrons in the bulk or at the surface, play an important role in the properties of materials, and have generated the field of "plasmonics." We report the observation of a highly unusual acoustic plasmon mode on the surface of a three-dimensional topological insulator (TI) Bi_{2}Se_{3}, using momentum resolved inelastic electron scattering. In sharp contrast to ordinary plasmon modes, this mode exhibits almost linear dispersion into the second Brillouin zone and remains prominent with remarkably weak damping not seen in any other systems. This behavior must be associated with the inherent robustness of the electrons in the TI surface state, so that not only the surface Dirac states but also their collective excitations are topologically protected. On the other hand, this mode has much smaller energy dispersion than expected from a continuous media excitation picture, which can be attributed to the strong coupling with surface phonons.