The lowest three or four excited states (the triplet or quartet states) of the Cu atom in a neon (Ne) matrix have been studied experimentally, and have been presumed to have the electronic configuration of Cu 4p(1). The origins of the triplet and the quartet are not yet fully clear, although many models have been proposed. It has been argued, for example, that the existence of different trapping sites would give rise to two partly overlapping triplets, leading to spectra having three or four lines or more. Below, the electronic structures of the ground state and lowest excited states of the Cu atom in the neon matrix are clarified by means of ab initio molecular orbital calculations, using the cluster model. It was found that a rather large vacancy (hollow) with residual Ne atoms is vital for explaining the observed spectra having three or more lines; the Cu atom occupies the center of the substitutional site of a face-centered cubic (fcc)-like cluster comprising 66 Ne atoms, in which the first shell composed of 12 Ne atoms is empty. The presence of the residual Ne atoms in the first shell gives rise to more than three excited states, explaining the experimental spectra. Electron-electron interaction (including the crystal field) and spin-orbit interaction are both important in explaining the experimental spectra.