DFT(B3LYP) calculations on the spectroscopic properties of the low-lying states of CuO and CuO- have been carried out. The corresponding electronic spectrum has been estimated by using MRSDCI, MP4(SDQ) and CCSD(T) methods. The results support the assignment, based on the recent photoelectron spectroscopic (PES) experiment that the state at 1.91 eV is a CuO((4)Sigma(-)) and the CuO((2)Delta) arising from the electron detachment of a 3d electron of CuO- is more than 2.2 eV above the ground state of CuO(X (2)Pi). Our calculations suggest that the feature a' in the PES experiment of CuO- should be due to the 1 (1)Pi excited state, rather than due to the spin-orbit splitting component of the 1 (3)Pi state as suggested in the PES experiment.