The free damped vibration signal of engineering structures is an energy-limited signal, and the effective signal length is limited by the damped factor. The classical periodic graph method is affected by signal damped coefficient and noise, and it is difficult to obtain satisfactory recognition accuracy. This article proposes the IEAI method for frequency estimation of freely damped vibration signal, considering the influence of initial phase. By combining discrete Fourier transform with complex operations, the signal is iteratively interpolated to improve the accuracy of frequency estimation .The simulation results show that the mean error of the IEAI method is 1.3%~26.5% of the traditional Periodogram method, A&M method and Welch method, and the Root-mean-square deviation is 7.4%~40.3% of the latter three methods under the condition of high signal-to-noise ratio; In the case of low signal-to-noise ratio, the mean error of the IEAI method is 16.2%~43.0% of the latter three, and the Root-mean-square deviation is 20.8%~81.8% of the latter three. The experimental results of cantilever beam damage identification show that the IEAI method is more sensitive to small structural damages and can be used for the identification and diagnosis of small structural damages.