The photoionization cross section of the ground state 2s 2 2p 2 P o 1/2 and the first excited state 2s 2 2p 2 P o 3/2 of C II ions are systematically calculated using the fully relativistic R-matrix code DARC. The detailed resonances are presented and identified for the photon energy ranging from threshold (24.38 eV) up to 41.5 eV where the L-shell (2p, 2s) photoionization process is dominant. In the calculations, the relativistic effect and electronic correlation effect are well considered. It is found that the relativistic effect is very important for the light atomic system CII, which accounts for experimentally observed fine structure resonance peaks. A careful comparison is made between the present results and the experimental values, and also other theoretical data available in the literature, showing that good agreement is obtained for the resonance peaks.