Electronic structure and optical properties of ZnO doped with carbon have been investigated by using density functional theory based on first-principles ultrasoft pseudopotential method. The calculated results show that there is a significant difference in electronic structures between the cases of C substituting O and C substituting Zn in ZnO,which is caused by both the electronic structure of C atom and its interaction with the neighboring atoms. We also find that the optical properties are charged in the low-energy region after doping, while in the high-energy region the optical properties are almost not influenced by doping with C. The changes of optical properties are qualitatively explained in connection with the calculated electronic structure.