Single-ended travelling wave fault location methods have the advantages of avoiding the complexities and costs of the remote-end synchronisation. However, the determination of the arrival time of the travelling wave and its corresponding propagation velocity is a difficult problem which is apt to limit the algorithms' accuracy. A novel single-ended fault location method based on travelling wave time-frequency characteristics for transmission lines is proposed in this study. The time-frequency characteristics of the travelling wave signal are described by the Lipschitz exponent. The Lipschitz exponent of the second transient wave-front signal is estimated by using the wavelet transform and the least square method. Extensive simulations have been carried out in PSCAD/EMTDC, and the results demonstrate that the accuracy of the proposed fault location method is significantly improved comparing with that of the traditional travelling wave fault location method. The proposed method is insensitive to different fault conditions, and it adapts to both transposed and untransposed lines well.