The holographic connection between strongly-coupled gauge theories and extra-dimensional gravitational theories has succeeded in describing many features of non-perturbative QCD. Phenomenological models called AdS/QCD use a five-dimensional AdS black hole to study thermodynamic properties of the quark-gluon plasma. In this talk, we focus on the phase transition that occurs as chiral symmetry is restored at high temperature and chemical potential. Using a Reissner-Nordström metric for a charged black hole, we find a critical temperature around 150 MeV and a critical quark chemical potential around 560 MeV. We qualitatively reproduce the Columbia plot, showing the dependence of the phase transition order on the light and strange quark masses. We show that the introduction of a chemical potential does not affect the order of the phase transition, implying the absence of a critical point in this simple model.