We explore the excitonic effects in chiral graphene nanoribbons(cGNRs), whose edges are composed alternatively of armchair-edged and zigzag-edged segments. For cGNRs dominated by armchair edges, their energy gaps and exciton energies decrease with increasing chirality angles, and they, as functions of widths, oscillate with the period of three, while the exciton binding energies do not have such distinct oscillation. On the other hand,for cGNRs dominated by zigzag edges, all the energy gaps, exciton energies, and exciton binding energies show oscillation properties with their widths, due to the interactions between the edge states localized at the opposite zigzag edges. In addition, the triplet excitons are energy degenerate when the electrons are spin-unpolarized,while the degeneracy split when the electrons are spin-polarized. All the studied cGNRs show strong excitonic effects with the exciton binding energies of hundreds of meV. We explore the excitonic effects in chiral graphene nanoribbons (cGNRs), whose edges are composed alternatively of armchair-edged and zigzag-edged segments. For cGNRs dominated by armchair edges, their energy gaps and exciton energies decrease with increasing chirality angles, and they, as functions of widths, oscillate with the period of three, while the exciton binding energies do not have such distinct oscillation. On the other hand, for cGNR dominated by zigzag edges, all the energy gaps, exciton energies, and exciton binding energies show oscillation properties with their widths, due to the interactions between the edge states localized at the opposite zigzag edges. The addition of the electrons excitons are energy degenerate when the electrons are spin-unpolarized, while the degeneracy split when the electrons are spin-polarized. the studied cGNRs show strong excitonic effects with the exciton binding energies of hundreds of meV.