We discuss the Sakai-Sugimoto model at finite temperature and finite chemical potential. It is a holographic model of large N_c QCD with N_f massless quarks based on a D4/D8-D̅8̅ brane system. The near horizon limit of the D4-branes and the probe approximation of the D8-D̅8̅ pairs allow us to treat the D4-branes as a gravitational background and the D8-D̅8̅ pairs as a probe which does not affect the background. We propose that the asymptotic value of a U(1) gauge field on the D8-D̅8̅-branes is identified with the chemical potential for the baryon number. Using this chemical potential we analyze the phase structure of this model and find a chiral symmetry phase transition of the first order.