Spectroscopic ellipsometry (SE) measurements coupled with efficient theoretical modeling and scanning electron microscopy analysis are used in the metrology of randomly-distributed gold nanoparticles on a multilayer film. Measurements were conducted in the ultraviolet to near infrared region at several angles of incidence. To understand the size, shape, and distribution of nanoparticles, a finite-element Green's function approach considering the scattering from multiple nanoparticles was employed to calculate the ellipsometry parameters. Our calculations are in fair agreement with the ellipsometry measurements when suitable size, shape, and distribution pattern of nanoparticles are found. This demonstrates that SE could be a useful tool to the metrology of arbitrarily-distributed nanoparticles on a multilayer film.