Pure and Cu doped ZnO nanorods array are synthesized via two step chemical bath deposition method. The seed layer is prepared by successive ionic layer adsorption reaction (SILAR) method. The synthesized materials have been systematically characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray (EDAX), Raman spectroscopy, Fourier transform infrared (FTIR) spectroscopy and photoluminescence (PL) spectroscopy. SEM pictures show the existence of vertically well aligned hexagonal ZnO nanorods. EDAX spectrum confirms the presence of Cu in ZnO nanorods. High intense peak of (002) plane and E2high mode for XRD and Raman spectrum respectively, suggest the ZnO nanorods are adopted c-axis orientation perpendicular to substrate. XRD and Raman analysis shows the presence of tensile strain in Cu doped ZnO nanorods. Effect of Cu doping on lattice constants, unit cell volume and Zn–O bond length of ZnO nanorods have also been studied. Room temperature PL measurement exhibits two luminescence bands in the spectra i.e. UV emission centered at 3.215eV and a broad visible band. Theoretical investigation for capping action of triethanolamine is done by Hartree–Fock(HF) method with 3-21G basis set using Gaussian 09 program package.