The commonly used fault diagnosis method of the power transmission line (PTL) is the traveling wave method which uses the traditional mode components $$\alpha $$ , $$\beta $$ and o to realize the fault type recognizing and the fault location in distribution network. However, the traditional mode components of the traveling wave method may take the value of zero that cannot provide the effective fault feature for the A-phase ground fault, or the A and B double phases short-circuit fault. Moreover, a single traditional mode component cannot recognize all the types of the faults, and the fault recognition has to use the multiple mode components that increases the complexity. To address the aforementioned issues, this paper proposes an edge computing scheme based on a novel mode component $$\gamma $$ for PTL fault diagnosis in distribution network. Firstly, the novel mode component $$\gamma $$ is fused according to the traditional mode components $$\alpha $$ and $$\beta $$ , then the propagation property of the traveling wave- $$\gamma $$ is derived. Secondly, the edge computing scheme and the PTL fault diagnosis method are designed for distribution network by using the only novel mode component $$\gamma $$ . Thirdly, the relationship table of the fault type and the boundary conditions as well as the component $$\gamma $$ expressions is derived for the fault recognition using the only traveling wave- $$\gamma $$ . In addition, the fault distance computing is explored by using the traveling wave- $$\gamma $$ . The computing is composed with the wave- $$\gamma $$ head identification using the optimal Wavelet vanishing moment parameter, and the arrival time determination, and the fault location method. To evaluate the efficiency of the proposed edge computing scheme, the simulation experiment and the laboratory tests are conducted. The simulation experiment results show that, the novel mode component $$\gamma $$ not only provides the effective fault features for all the ten types of the power transmission line faults, but also increases fault locating accuracy by the average 2.08 % compared with the methods using the traditional mode component $$\alpha $$ , $$\beta $$ and o. Meanwhile, the laboratory tests show that the edge computing method is practical.