Damage identification for a cantilever beam with a breathing crack was presented based on instantaneous frequency(IF). One time-varying stiffness model was introduced by considering the breathing effect of the crack in vibration. A simplified single-degree-of-freedom(SDOF) time-varying dynamic differential equation was built. Relationships between the structural instantaneous frequencies (IFs) and damage location and degree were analyzed. IFs of the free vibration displacements were estimated by using phase difference and Teager energy operator (TEO).Moreover the influence of noise on IFs estimation was discussed. Damage indices were built by IFs and the damage degree was identified. Structural IFs are two-dimension function of damage location and degree and the intra-wave phenomenon of IFs verified the non-linearity of damaged structure. The damage indices based on IFs are more reliable than traditional frequency on identifying damage degree and have some anti-noise properties.