The study of asteroids that present sporadic cometary activity, is of fundamental importance to address several astronomical problems like the end states of comet nuclei, the abundance of water in main belt asteroids and its role as a possible source of terrestial water. 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. We report visible and near infrared spectra covering the 0.35-2.4 micron spectral range, obtained with the 4.2m William Herschel Telescope, the 2.5m Nordic Optical Telescope and the Italian 3.58m Telescopio Nazionale Galileo at "El Roque de los Muchachos" Observatory (La Palma, Spain). The spectrum is compared with that of meteorites samples and man-made mineral mixtures to determine possible components, and modeled using multiple scattering formulations. It is also compared with the spectra of comet nuclei and other comet-asteroid transitional objects. Phaethon's spectrum does not show any sharp structure and has a negative slope at wavelengths >0.43 microns, consistent with a B-type asteroid. Below 0.43 microns the reflectance decreases. Its shape is similar to that of aqueously altered CI/CM meteorites and 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. 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 Main Belt Comets reported by Hsieh & Jewitt (2006), than an extinct comet.