The band structure and dielectric function of a (6,6) single-walled zinc oxide nanotube (SWZONT) have been studied using the first-principles method within the pseudopotential density functional theory (DFT). We find that the (6,6) SWZONT has a direct band gap with an energy gap of 1.91eV. The valence bands (VBs) are composed of two parts, namely, the low-energy part and the high-energy part. The dielectric function indicates a moderate optical anisotropy in the SWZONT. The magnitude of the peaks in the ε 2 (ω) spectrum of dielectric function for the [100] direction is about half of the magnitude of the corresponding ones for the [001] direction, which is similar to the case found in single-walled boron nitrogen nanotubes (SWBNNTs). However, the character of dielectric function is different with that of single-walled carbon nanotubes (SWCNTs).