[en] We study the collective excitations of Na₂IrO₃ in an itinerant electron approach. We consider a multi-orbital tight-binding model with the electron transfer between the Ir 5d states mediated via oxygen 2p states and the direct d–d transfer on a honeycomb lattice. The one-electron energy as well as the ground state energy are investigated within the Hartree–Fock approximation. When the direct d–d transfer is weak, we obtain nearly flat energy bands due to the formation of quasimolecular orbitals, and the ground state exhibits the zigzag spin order. The evaluation of the density–density correlation function within the random phase approximation shows that the collective excitations emerge as bound states. For an appropriate value of the direct d–d transfer, some of them are concentrated in the energy region $\mathrm{\omega <!--\; ??\; -->}<50$ meV (magnetic excitations) while the others lie in the energy region $\mathrm{\omega <!--\; ??\; -->}>350$ meV (excitonic excitations). This behaviour is consistent with the resonant inelastic x-ray scattering spectra. We also show that the larger values of the direct d–d transfer are unfavourable in order to explain the observed aspects of Na₂IrO₃ such as the ordering pattern of the ground state and the excitation spectrum. These findings may indicate that the direct d–d transfer is suppressed by the structural distortions in the view of excitation spectroscopy, as having been pointed out in the ab initio calculation. (paper)