The invention discloses a method of calculating the travelling wave front of a single-phase grounding fault in a distribution network. A line data collector uploads two voltage cycles before a fault and two voltage cycles after the fault, performs Karrenbauer transform on the voltage travelling wave to get a line mode voltage, performs Hilbert transform on the line mode voltage, carries out derivation, and calculates the modulus. The obtained modulus is de-noised, an effective interval is taken, and then, the arrival time of the travelling wave front is obtained. The method has the advantage of quick and accurate calculation. Through the method, the arrival time of the travelling wave front can be calculated accurately, and conditions can be created for fault location. The method has a very good application prospect.