We investigated optical properties of several 2D arrangements of Au nanoparticles (NPs), including dimer, trimer, hexamer, and heptamer, using finite-difference time-domain method. The heptamerous system, consisting of a central NP and six NPs forming a hexagonal shape, exhibited Fano resonance. We found that the intensity and position of the Fano resonance peak depended on the size of the central NP and its distance from the other six NPs. Furthermore we studied 3D configurations, where the location of the central NP was moved along the perpendicular direction to the plane containing the other NPs. Such vertical displacement of the central NP influenced the plasmonic coupling between NPs and affected the extinction spectra. Such 3D NP systems could provide us alternative approaches to tune the optical properties of the plasmonic NPs.