We report on spatially resolved electron energy-loss spectroscopy studies of optical modes in individual star-shaped gold nanoparticles. We studied different morphologies, ranging from a spheroid to well-developed nanostars. For each shape, essentially two groups of modes are appearing: the first one is localized around the core of the nanostars and has an energy slightly less than the quasi-static dipolar mode of a gold sphere (about 2.2 eV); in the second group, the modes are localized at the end of the nanostar tips, with varying energies depending on the geometry of each tip and with energy down to 1.2 eV. The localization of the tip modes is interpreted with the help of boundary element methods simulations.