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 7 electron excitation of the pyrrole rings and the shoulder peak comes from the charge transfer from Asp87 (a nearby amino acid residue) to PCBH+.