Fault　classification　is　important　for　the　fault　cause　analysis　and　faster　power　supply　restoration.　A　deep-learning-based　fault　classification　method　in　small　current　grounding　power　distribution　systems　is　presented　in　this　paper.　The　current　and　voltage　signals　are　sampled　at　a　substation　when　a　fault　occurred.　The　time-frequency　energy　matrix　is　constructed　via　applying　Hilbert-Huang　transform　(HHT)　hand-pass　filter　to　those　sampled　fault　signals.　Regarding　the　time-frequency　energy　matrix　as　the　pixel　matrix　of　digital　image,　a　method　for　image　similarity　recognition　based　on　convolution　neural　network　(CNN)　is　used　for　fault　classification.　The　presented　method　can　extract　the　features　of　fault　signals　and　accurately　classify　ten　types　of　short-circuit　faults,　simultaneously.　Two　simulation　models　are　established　in　the　PSCAD/EMTDC　and　physical　system　environment,　respectively.　The　performance　of　the　presented　method　is　studied　in　the　MATLAB　environment.　Various　kinds　of　fault　conditions　and　factors　including　asynchronous　sampling,　different　network　structures,　distribution　generators　access,　and　so　on　are　considered　to　verify　the　adaptability　of　the　presented　method.　The　results　of　investigation　show　that　the　presented　method　has　the　characteristics　of　high　accuracy　and　adaptability　in　fault　classification　of　power　distribution　systems.