The optical properties of self-assembled gold nanoparticles on silicon substrate have been determined using ellipsometric analysis. The dielectric function of the nanoparticles is best represented by a Drude term and three Lorentz oscillators with the resonance energies at 1.26, 2.22, and 3.65 eV. The Lorentz oscillator at 3.65 eV is due to the interband transitions, while the other two oscillators are attributed to the splitting of the plasmon resonance of the spatially limited free electrons inside the nanoparticles. The splitting of plasmon resonance could be due to the influence of various factors such as the near-field interactions of adjacent nanoparticles, image effects of the substrate, imperfect spherical shapes of the nanoparticles, etc.