In　this　paper,　we　proposed　an　direction-of-arrival　(DOA)　estimation　method　based　on　difference　L-1　and　L-2　minimization.　The　dictionary　is　highly　coherent　in　the　application　of　DOA　estimation,　which　brings　about　challenges　to　sparse　signal　reconstruction　algorithms.　Difference　of　L-1　and　L-2　behaves　closer　to　L-0　than　L-p　(0　＜　p　＜　2),　and　is　able　to　produce　better　result　in　the　case　of　highly　coherent　dictionary.　Therefore,　the　better　results　are　achievable　when　difference　L-1　and　L-2　minimization　is　employed　to　DOA　estimation.　In　addition,　the　nested　array　is　adopted　in　our　method　to　improve　the　degrees　of　freedom　(DOF).　Simulation　results　illustrate　that　our　method　performs　better　than　L-p　minimization　and　spatial　smoothing　(SS)-MUSIC　when　snapshots　are　shortage.