We have studied electromagnetic field on the surface of two-dimensional nanostructure of gold nanoparticles through two-photon-induced photoluminescence images by using scanning near-field optical microscope and far-field surface-enhanced Raman scattering measurements. The near-field two-photon-induced photoluminescence image shows that strong inhomogeneous enhancement in two-photon-induced photoluminescence occurs over the two-dimensional nanostructure, representing localized surface plasmon excitations. The results suggest that the local structure of the two-dimensional nanostructure influences the distribution of localized surface plasmon excitation.