Aims: In this paper we establish a compositional and dynamical connection between two B-type objects: main belt asteroid (2) Pallas and near-Earth asteroid (3200) Phaethon. The final purpose is to help understand the origin of this very interesting object. Methods: We first compare visible and near-infrared spectra of asteroids Phaethon and Pallas. We then compare the reflectance spectra of Phaethon with all the available visible spectra of B-type asteroids belonging to the Pallas family. One last spectral comparison is then performed to search for any correspondence between Phaethon and any B-type asteroid in the main belt. Numerical simulations are also carried out to explore the dynamical connection between the orbital neighborhoods of Pallas and Phaethon. Results: Main differences between Phaethon and Pallas lie in the visible wavelength part of their reflectance spectra. We have also found that the nine asteroids belonging to the Pallas family have visible spectra that are different from that of Pallas and strikingly similar to that of Phaethon. Spectral comparison excludes any other B-type asteroid in the main belt as a possible parent body of Phaethon. Numerical simulations establish a dynamical pathway that connects Phaethon with Pallas and its family members. Conclusions: The spectral similarities between Phaethon and Pallas family members, together with their established dynamical connection, supports Pallas as the most likely parent body of Phaethon and therefore, the associated Geminids meteor stream. We suggest that differences in asteroid sizes are the most likely explanation for the differences in the visible reflectance spectra between Phaethon and Pallas.