The single-ended fault location based on travelling waves (TWs) is commonly used for long-distance high-voltage AC transmission lines. However, it relies on high sampling frequency and accurate capturing of the TW head arrival time. Accordingly, this study establishes a transient analytical method for fault location based on the similarity between the transient recorded waveform and output waveforms of analytical calculation model. In the proposed method, fuzzy constraints of fault features are constructed through time-distance and waveform-scaling correlations while considering the deviation factors of the frequency-dependent wave velocity and TW head arrival time. Accordingly, the high-dimensional space of the fitting problem is transformed into a one-dimensional implicit function fitting problem containing only the fault distance, thereby enabling the waveform comparison problem to be quickly solved based on fault TW features. Under the fuzzy constraints proposed in this study, the proposed method requires only a relatively vague identification of the TW head, and the requirements for sampling frequency are also more lenient. In addition, a sliding window scheme is adopted for enhancing the TW morphology characteristics. Finally, the proposed method is tested using PSCAD, and the simulations validate the fault location accuracy of the proposed method.