The aim of this paper is to propose a robust method for extracting damping ratios of a railway contact wire using a continuous wavelet transform (CWT). It is hard to measure the damping ratios of the contact wire because the contact wire has close natural modes in a low frequency range and the dynamic signals of the contact wire gathered in the field are easily corrupted by extraneous noises. The proper choice of the wavelet parameters to decouple the close modes is required in order to obtain accurate damping ratios for the railway contact wire. In this paper, we investigated CWT error terms and derived a relation between a frequency resolution and complex Morlet wavelet parameters. In order to show the accuracy of the proposed method, we extracted damping ratios for the simulated pure and noisy signals which have close natural modes. According to the results, the proposed method can provide the damping ratios well agreed with true ones even for the noisy data. Finally, we applied the proposed method to the contact wire of a conventional railway line in Korea in order to verify the applicability in the field. The damping ratios extracted from the real data were in the range from 0.01 to 0.04.