A grating spectrometer equipped with a photomultiplier was used to measure atmospheric optical depth with the moon as an extraterrestrial light source. Measurements are presented in the window regions in the spectral range 0.32-0.64 mu m, with a resolution of about 3 nm. The Langley method was applied to estimate atmospheric optical depth. Measurements have been performed at a mountain site in southern Italy, at 1247 m above sea level in the context of the Gamma-ray Air-Cherenkov Multi Telescope experiment.