Electromagnetic resonant absorption phenomena in highly anisotropic superconductor Bi2Sr2CaCu2O8 has been studied at a microwave frequency region of 35 GHz. The sharp resonance observed as a function of magnetic field can be interpreted as a plasma resonance of superconducting electrons. Making use of the difference in the dispersion relation of the two plasma modes, which gives rise to the clear sample size dependence, we are able to distinguish the longitudinal mode from the transverse one in a cavity resonator with TE102 mode. Since the longitudinal plasma mode is the Nambu-Goldstone (NG) mode in a superconductor in the context of the spontaneous symmetry breaking of the gauge field, the experimental observation of the longitudinal plasma mode clearly verifies for the first time the existence of the NG bosons in a superconductor. The finite plasma gap can be interpreted by the possession of mass of NG bosons in accordance with the Anderson's conjecture.