The frequency equation for the localized mode of one dimensional photonic crystal with a nonlinear defect is exactly derived by means of a transfer matrix method. The localized mode frequency depends on the localized light intensity. With the increase of the localized light intensity, the localized mode frequency will arise from the lower edge of the gap, then increase, and vanish near the upper edge of the gap for the case that Kerr coefficient is negative. When incident light frequency is given, with the varing incident light intensity, the system exhibits bistability. The bistability feature is due to the shifting of the localized mode frequency.