  We provide a method to study hadronic matter at finite density in the context
of the Sakai-Sugimoto model. We introduce the baryon chemical potential through
the external $U(1)_v$ in the induced (DBI plus CS) action on the
D8-probe-brane, where baryons are skyrmions. Vector dominance is manifest at
finite density. We derive the baryon density effect on the energy density, the
dispersion relations of pion and vector mesons at large $N_c$. The energy
density asymptotes to a constant at large density suggesting that dense matter
at large $N_c$ freezes, with the pion velocity dropping to zero. Holographic
dense matter enforces exactly the tenets of vector dominance, and screens
efficiently vector mesons. At the freezing point the $\rho-\pi\pi$ coupling
vanishes with a finite rho mass of about 20% its vacuum value.
