Context: The study of asteroids that present sporadic cometary activity is of fundamental importance to address several astronomical problems including the end states of comet nuclei, the abundance of water in main belt asteroids, and its role as a possible source of terrestial water. Aims: We studied the composition of the surface of asteroid (3200) Phaethon, a paradigmatic case of asteroid-comet transition object, in order to determine its cometary or asteroidal nature. Methods: We report visible and near infrared spectra covering the 0.35-2.4 μm spectral range, obtained with the 4.2 m William Herschel Telescope, the 2.5 m Nordic Optical Telescope, and the Italian 3.58 m Telescopio Nazionale Galileo at "El Roque de los Muchachos" Observatory (La Palma, Spain). Our spectrum is compared with those of meteorite samples and man-made mineral mixtures to determine possible components, modeled using multiple scattering formulations, and also compared with the spectra of comet nuclei and other comet-asteroid transitional objects. Results: Phaethon's spectrum does not show any sharp structure and has a negative slope at wavelengths >0.43 μm, consistent with B-type asteroids. Below 0.43 μm the reflectance decreases. The spectral shape is similar to that of aqueously altered CI/CM meteorites and of hydrated minerals. A surface composition with hydrated silicates is also suggested by the models. A possible spectral variability in the UV is suggested by the avaliable spectra, and is compatible with a slightly different abundance of hydrated silicates. Finally, Phaethon's spectrum shows important differences with the few comet nuclei properly observed at these wavelengths and is similar to the spectra of other peculiar comet-asteroid transition objects. Conclusions: .The spectral properties and dynamical properties of (3200) Phaethon support an asteroidal nature rather than a cometary one. Phaethon is more likely an "activated" asteroid, similar to the population of activated asteroids in the Main Belt Comets, than an extinct comet.