||The largest natural source of light at night is the Moon, and it is the major contributor to the astronomical sky background. Being able to accurately predict the sky background, including scattered moonlight is important for scheduling astronomical observations. We have developed an improved scattered moonlight model, in which the components are computed with a better physical understanding as opposed to the simple empirical fit in the frequently used photometric model of Krisciunas & Schaefer (1991, PASP, 103, 1033). Our spectroscopic model can better trace the spectral trends of scattered moonlight for any position of the Moon and target observation. This is the first scattered moonlight model that we know of which is this physical and versatile. We have incorporated an observed solar spectrum, accurate lunar albedo fit, and elaborate scattering and absorption calculations that include scattering off of molecules and aerosols. It was designed for Cerro Paranal, but can be modified for any location with known atmospheric properties. Throughout the optical range, the uncertainty is less than 20%. This advanced scattered moonlight model can predict the amount of scattered moonlight for any given geometry of the Moon and target, and lunar phase for the entire optical spectrum.