We have investigated the excitation spectra of j(eff) = 1/2 Mott insulator Na2IrO3. Taking into account a relativistic multiplet structure of Ir ions, we have calculated the optical conductivity sigma(omega) and resonant inelastic x-ray scattering (RIXS) spectra, which manifest different features from those of a canonical j(eff) = 1/2 system Sr2IrO4. Distinctly from the two-peak structure in Sr2IrO4, sigma(omega) in Na2IrO3 has a broad single peak dominated by interband transitions from j(eff) = 3/2 to 1/2. RIXS spectra exhibit the spin-orbit (SO) exciton that has a two-peak structure arising from the crystal-field effect, and the magnon peak at energies much lower than in Sr2IrO4. In addition, a small peak near the optical-absorption edge is found in RIXS spectra, originating from the coupling between the electron-hole (e-h) excitation and the SO exciton. Our findings corroborate the validity of the relativistic electronic structure and importance of both itinerant and local features in Na2IrO3.open1122sciescopu