In combination with short circuit simulation and wavelet packet theory, the corresponding probabilistic analysis on the characteristics of single-phase grounding faults of distribution network under stochastic context is studied in this paper. There are two pieces of major research works: firstly, the Latin hypercube sampling (LHS) method is adopted to accelerate probabilistic short circuit analysis, thus improving the efficiency for a further implementation; secondly, wavelet packet method is employed to investigate the influence of stochastic factors on the characteristics of short circuit and fault line identification. Test results verify the effects of the works, as well as some conclusions are drawn.