According to the spin-polarized density functional theory, we study the electronic structures, the magnetic and the optical properties of Cr-doped ZnO nanowires. The calculated results show ferromagnetic coupling for Cr atoms substitution for Zn atoms in ZnO nanowires along the [0001] direction, and the antiferromagnetic coupling with Cr-doped in ZnO nanowires along the [1010] and [0110] directions. The results reveal that the magnetic coupling state near the Fermi level gives rise to such a spin splitting phenomenon near the Fermi level, which indicates that Cr 3d and O 2p orbitals have intense hybrid effects. In addition, the spin electronic density results indicate that system magnetic moments are generated mainly by the unpaired 3d electrons of Cr atoms and are also related to the electron configuration. Moreover, the results of optical properties show that the obvious absorption peaks are observed in the far ultraviolet and the near ultraviolet regions and there is a red shift phenomenon in the ultraviolet region. These results indicate that the Cr-doped ZnO nanowires could be a promising dilute magnetic semiconductor material.