We have investigated photoionization of the C2+ ion by using the multiconfiguration relativistic random-phase approximation theory. Precise energies and widths of all five Rydberg series of doubly-excited states (2pns)3,1P1o , (2pnd)3,1P1o , and (2pnd)3D1o are given in the photon-energy region between (1s2 2s)2S1/2 and (1s2 2p)2P1/2 ionization thresholds. Comparisons with previous theoretical works and experimental measurements are also made.