The optical properties of thin gold films with thickness varying from 2.5 nm to 30 nm are investigated. Due to the quantum size effect, the optical constants of the thin gold film deviate from the Drude model for bulk material as film thickness decreases, especially around 2.5 nm, where the electron energy level becomes discrete. A theory based on the self-consistent solution of the Schrödinger equation and the Poisson equation is proposed and its predictions agree well with experimental results.