In this paper, the geometrical, elastic, electronic, phonon, and optical properties of Na3AgO2 have been systematically studied by first-principles calculation. The results show that Na3AgO2 is mechanically stable and has small compressibility. Na3AgO2 is an indirect band-gap semiconductor with weak interatomic interaction. The bandgap calculated by HSE06 is 2.314 eV, and that calculated by GGA is 1.261 eV. For Na3AgO2, in the valence band near the Fermi level, the curve peaks of TDOS at −2.11 eV and −0.885 eV are primarily composed of O 2p states, which hybridize the 4 d and 4p states of Ag. The conduction band mainly consists of the 4p, 4 d, and 5s states of Ag, while hybridizing a few 2p states of O and a few 2p and 3s states of Na. As can be seen from the phonon dispersion spectrum there is no negative phonon frequency in the whole Brillouin region, indicating the structure is stable. Mulliken bond population of Na3AgO2 shows that O–Ag bonds have strong covalency, O–Na bonds have strong ionic properties, Na–Na bonds and Na–Ag bonds are antibonding. Na3AgO2 has a small reflectivity and a small absorption coefficient in the direction of (100) and (010) and has good transparency. The transparency of blue-violet light in the (001) direction is not as good as that of low-energy visible light. The obtained results lead to the conclusion that Na3AgO2 is a promising p-type transparent conducting material and is expected to be applied in practice.