At present, the influence of arc length variation on an arc fault in a distribution network is mostly ignored. The arc fault model is quite different from the actual arc fault in a distribution network, and the identification of an arc grounding fault is inaccurate. Therefore, in this paper, an arc grounding fault model considering arc length dynamic variation is established. The time-domain waveform difference of the steady-state zero-sequence current of an arc grounding fault is analyzed, and an identification method for the fault based on weighted Euclidean distance of the steady-state zero-sequence current is proposed to realize effective identification. A 10 kV distribution network model is built using PSCAD. A large number of arc grounding fault simulation results show that the model presented is accurate and effective, and can accurately describe the arc current, voltage and fault characteristics. The identification method can accurately identify all of fault types, and is not affected by the fault initial phase angle and fault location. This provides a reliable basis for accurate and reliable perception of distribution network faults. This work is supported by the Science and Technology Project of State Grid Corporation of China (No. J2021032).