The complex refractive index of Diamond-like Carbon (DLC) thin films, which can be applied to optical devices or electrical devices, have been determined using optical methods. DLC thin films are grown on Si(100) substrates and vitreous silica substrates respectively, using the technique of plasma enhanced chemical vapor deposition (PECVD). The spectroscopic ellipsometry data($psi$, $Delta$) and the transmission spectra of these DLC films are obtained. These optical spectra are analyzed with the help of the Sellmeier dipersion relation and a quantum mechanically derived dispersion relation. Using spectroscopic ellipsometry data at their transparent region, the refractive index and the effective thickness of DLC films on vitreous silica are model calculated, Then the transmission spectra are inverted to yield the extinction coefficient spectra k(λ) at absorbing region. These spectra are fit to the quantum mechanical dispersion relation and the best fit dispersion constants are determined. The complex refractive indices are easily calculated with these constants. The spectroscopic ellipsometry data at the absorbing region in model calculated to give the packing densities and the degrees of surface microroughness of DLC films. Discussions are made in correlation with the growth condition of DLC films.