Copper cysteamine (Cu-Cy) is a new type of photosensitizer, which can be activated not only by ultraviolet light, but also by X-rays, microwaves and ultrasound to generate reactive oxygen species for treating cancer and infection diseases. Moreover, copper cysteamine has a strong luminescence, which can be used for both therapeutics and imaging. In addition, it can also be used for solid state lighting, radiation detection and sensing. However, its electronic structures, and particularly its excited states, are not yet clear. Here, we present a computational study aiming to determine the nature of the excited states involved in the photophysical processes that lead to the luminescence of this compound. This study has been conducted using density functional theory (DFT), using both hybrid functionals and time-dependent DFT. It is found that both absorption and emission involve the replacement of an electron among the 3d and 4s orbitals of one or the other of the two types of Cu atoms found in the system. Our computed results compared well with the experimental absorption and emission results. These results are very helpful for the understanding of the experimental observations.