An accurate and effective technology for fault diagnosis of a high-voltage transmission line plays an important role in supporting rapid system restoration. The fault diagnosis of a high-voltage transmission line involves three major tasks, namely fault-type identification, fault location and fault time estimation. The diagnosis problem is formulated as an optimisation problem in this work: the variables involved in the fault diagnosis problem, such as the fault location, and the unknown variables such as ground resistance, are taken into account as optimisation variables; the sum of the discrepancy of the approximation components of the actual and expected waveforms is taken as the optimisation objective. Then, according to the characteristics of the formulated optimisation problem, the harmony search, an effective heuristic optimisation algorithm developed in recent years, is employed to solve this problem. Test results for a sample power system have shown that the developed fault diagnosis model and method are correct and efficient.