We report growth of the ZnO nanowires on graphene/SiO2/Si substrates using a chemical vapor deposition method. The length of nanowires varies from 1 microm to 10 microm with increasing the growth time from 30 min to 90 min. X-ray diffraction and high-resolution transmission electron microscopy investigations predict the high structural quality of the c-axis grown single crystalline ZnO nanowires. Temperature dependent photoluminescence spectra from the nanowires reveal excellent optical quality and excitonic behavior in the single crystalline ZnO nanowires. A well-resolved free exciton emission at 3.375 eV, indicates high crystalline quality nanowires and a strong PL peak at 3.370 eV is assigned to neutral-donor bound excitons (D0X).