The optical characteristics of absorption and circular dichroism (CD) spectroscopy of an alpha-subunit of C-phycocyanin (C-PC) were investigated by using time dependent density functional theory (TDDFT) combined with the polarizable continuum model (PCM). When the protonation of alpha-84 phycocyanobilin (PCB) and its interaction with the protein moiety in C-PC have been taken into account, satisfactory assignment of the absorption and CD spectra of alpha-84 PCB can be achieved. The TDDFT-PCM calculations conclude that in the visible absorption region the main peak arises from the pi electron excitation of the pyrrole rings and the shoulder peak comes from the charge transfer from Asp87 (a nearby amino acid residue) to PCBH(+).