The　sparse　decomposition　based　on　basic　pursuit　is　an　adaptive　sparse　expression　of　the　signals.　An　adaptive　basic　pursuit　algorithm　that　uses　an　impulse　dictionary　is　introduced　in　this　article　for　rolling　bearing　vibration　signal　processing　and　fault　diagnosis.　In　the　first,　a　new　dictionary　model　is　constructed　according　to　the　characteristics　and　mechanism　of　rolling　bearing　faults.　Rotational　speed　of　bearing,　dimensions　of　bearing　and　bearing　fault　situation,　among　other　parameters　incorporates　the　new　mode　which　could　simulate　the　real　fault　impulse　in　different　fault　levels.　Secondly　a　new　method　of　dictionary　establishment　called　adaptive　impulse　dictionary　combine　with　basic　pursuit　introduced　in　this　paper　for　bearing　fault　diagnosis.　Adaptive　impulse　dictionary　is　created　by　changing　characteristic　parameters　progressively,　which　make　the　dictionary　built　by　this　method　has　a　lower　redundancy　and　a　higher　relevance　between　each　dictionary　atom　and　the　analyzed　vibration　signal.　The　basic　pursuit　algorithm　of　an　adaptive　impulse　dictionary　is　adopted　to　analyze　experiment　signal　of　the　early-stage　fault　signals　and　composite　fault　signals　of　the　bearing.　The　results　demonstrate　the　effectiveness　of　the　basic　pursuit　algorithm　that　uses　the　adaptive　impulse　dictionary.